Algebra Calculator

Use this Algebra Calculator to solve common algebra problems and see the steps behind each answer. Choose a problem type, enter the known values, and the calculator will work through linear equations, quadratic equations, systems of equations, inequalities, expression simplification, factoring, and slope-intercept problems in a clear sequence.

The goal is not just to show a final number. Each mode explains the algebra used to reach the result so you can check homework, review Algebra 1 or Algebra 2, practice solving for x, and understand how equations change from one step to the next.

How to Use the Algebra Calculator

Choose the type of problem you want to solve. Each mode uses structured inputs so the calculator knows exactly what kind of algebra you are working with and can show dependable steps instead of trying to guess the meaning of an ambiguous expression.

For a linear equation, enter the coefficients in ax + b = c. For a quadratic, enter a, b, and c from ax² + bx + c = 0. The system solver accepts two equations in two variables. The inequality mode solves a one-variable linear inequality. Simplify combines like terms, Factor Quadratic finds real linear factors, and Slope & Line finds the equation through two points.

After you select Calculate, the answer appears first, followed by a numbered solution showing the main algebraic operations. This makes the tool useful for checking work rather than simply copying a result.

What Is Algebra?

Algebra is a branch of mathematics that uses numbers, variables, symbols, and operations to represent relationships. A variable such as x or y stands for a value that may be unknown, changeable, or part of a general rule.

Arithmetic asks questions such as 7 + 5. Algebra can ask what number added to 7 produces 12. Written as an equation, that becomes x + 7 = 12. Solving the equation means finding the value of x that makes the statement true.

Algebra is used throughout mathematics and in science, engineering, economics, finance, computing, statistics, construction, and many everyday calculations. It provides a way to turn a relationship into a formula that can be solved or reused.

Algebra 1 vs Algebra 2

Algebra 1 usually introduces variables, expressions, linear equations, inequalities, graphing lines, systems of equations, exponents, and basic polynomials. Algebra 2 builds on those topics with more advanced quadratics, polynomial functions, rational expressions, radicals, exponentials, logarithms, sequences, and other function types.

The calculator on this page focuses on the high-frequency core shared by Algebra 1 and Algebra 2: solving linear equations, quadratics, inequalities, systems, simplifying expressions, factoring, and working with slope.

How to Solve Algebra Equations

An equation says that two expressions are equal. Solving an equation means finding the value or values of the variable that keep both sides equal.

The central rule is balance: whatever operation you perform on one side of an equation must also be performed on the other side. If you subtract 5 from the left side, subtract 5 from the right. If you divide one side by 3, divide the other side by 3 as well.

This balance principle is the reason common equation-solving steps work. The objective is usually to undo operations around the variable until the variable is isolated.

Linear Equation Solver

A linear equation contains a variable to the first power. In one variable, a common form is ax + b = c. The graph of a two-variable linear equation is a straight line, which is where the word linear comes from.

To solve ax + b = c, first move the constant b away from the variable term by subtracting b from both sides. That produces ax = c – b. Then divide both sides by a, provided a is not zero.

The Linear Equation mode shows these operations explicitly. It also handles special cases. If the coefficient of x is zero and the remaining statement is true, the equation has infinitely many solutions. If the statement is false, it has no solution.

Solve for x

“Solve for x” is one of the most common instructions in algebra. It simply means rearrange the equation until x appears by itself on one side.

For 5x – 9 = 21, add 9 to both sides to get 5x = 30, then divide by 5. The result is x = 6. You can verify the answer by substituting 6 back into the original equation: 5(6) – 9 = 21.

Checking by substitution is one of the easiest ways to catch arithmetic mistakes. The calculator includes a check step for ordinary linear equations.

Equations With Fractions

Fractions can make an equation look more difficult than it is. One common strategy is to multiply every term by the least common denominator so the fractions disappear before solving.

For example, x/3 + 2 = 6 becomes x + 6 = 18 after multiplying every term by 3. Subtract 6 to get x = 12.

If you need to simplify or compare fractions separately, the Fraction Calculator can help with addition, subtraction, multiplication, division, and simplification.

Quadratic Equation Calculator

A quadratic equation contains a squared variable and can usually be written as ax² + bx + c = 0, where a cannot be zero. Quadratics can have two real solutions, one repeated real solution, or two complex solutions.

The calculator uses the quadratic formula because it works for every quadratic equation with numerical coefficients:

The quantity b² – 4ac is called the discriminant. It tells you what type of roots the quadratic has before the entire formula is evaluated.

Quadratic Formula Example

Consider x² – 5x + 6 = 0. Here a = 1, b = -5, and c = 6. The discriminant is (-5)² – 4(1)(6) = 25 – 24 = 1. Because the discriminant is positive, there are two real solutions.

Substituting into the quadratic formula gives x = (5 ± 1) / 2. The two solutions are x = 3 and x = 2.

Quadratic Roots and x-Intercepts

The real roots of a quadratic correspond to the x-intercepts of its graph when the quadratic is written as y = ax² + bx + c. If there are two real roots, the parabola crosses the x-axis twice. A repeated root means the parabola touches the x-axis once. Complex roots mean there are no real x-intercepts.

System of Equations Calculator

A system of equations contains two or more equations that must be true at the same time. The calculator solves a two-equation, two-variable system written as a₁x + b₁y = c₁ and a₂x + b₂y = c₂.

Geometrically, each equation represents a line. If the lines cross at one point, the system has one solution. Parallel lines have no solution. If both equations describe the same line, the system has infinitely many solutions.

The calculator uses determinant logic equivalent to elimination for a 2×2 system. It calculates the determinant of the coefficients and uses it to find x and y when the determinant is nonzero.

Substitution Method

Substitution solves a system by isolating one variable in one equation and replacing that variable in the other equation. For example, if x – y = 1, then x = y + 1. Substitute y + 1 for x in the second equation and solve for y.

Substitution is often convenient when one equation already has a variable with coefficient 1 or -1.

Elimination Method

Elimination adds or subtracts equations so one variable cancels. You may first multiply one or both equations so the coefficients become opposites.

For 2x + 3y = 12 and x – y = 1, multiplying the second equation by 3 gives 3x – 3y = 3. Adding the equations eliminates y, producing 5x = 15 and x = 3. Substituting x = 3 back into x – y = 1 gives y = 2.

Inequality Calculator

An inequality compares values using symbols such as <, >, ≤, or ≥ instead of an equals sign. Solving a linear inequality resembles solving a linear equation, with one crucial rule: multiplying or dividing both sides by a negative number reverses the inequality sign.

For example, -2x + 3 < 11 becomes -2x < 8 after subtracting 3. Dividing by -2 reverses the symbol, giving x > -4.

The result of an inequality is usually a range rather than one number. x > -4 means every real number greater than -4 satisfies the inequality.

Strict vs Inclusive Inequalities

The symbols < and > are strict inequalities, meaning the boundary value itself is excluded. The symbols ≤ and ≥ are inclusive, meaning the boundary value is part of the solution set.

On a number line, a strict boundary is usually drawn with an open circle, while an inclusive boundary uses a filled circle.

Simplifying Algebraic Expressions

Simplifying an expression means rewriting it in an equivalent but cleaner form. One of the first skills is combining like terms.

Like terms have the same variable raised to the same exponent. 3x and 5x are like terms, so they combine to 8x. But 3x and 5x² are not like terms because their exponents differ.

For 3x + 5 + 2x – 7, combine the x terms to get 5x and combine the constants to get -2. The simplified expression is 5x – 2.

Combining Like Terms

Only the coefficients are added or subtracted when like terms are combined. The variable part stays unchanged. 7x² – 3x² becomes 4x². Likewise, 4ab + 9ab becomes 13ab.

Constants are also like terms with each other. In 2x + 4 + 3x + 6, the x terms combine to 5x and the constants combine to 10.

Distributive Property

The distributive property is used to remove parentheses. The rule a(b + c) = ab + ac means the outside factor multiplies every term inside the parentheses.

For example, 3(x + 4) becomes 3x + 12. A negative sign must also distribute to every term: -(x – 5) becomes -x + 5.

Factoring Calculator

Factoring reverses multiplication. Instead of expanding two factors into a polynomial, factoring rewrites a polynomial as a product.

For a quadratic with real roots r₁ and r₂, the factored form can be written as a(x – r₁)(x – r₂). The calculator finds the roots first and then builds the factors from those roots.

For x² + 5x + 6, the roots are -2 and -3. Therefore the factored form is (x + 2)(x + 3). Expanding those factors produces x² + 5x + 6 again.

Greatest Common Factor

Before attempting more complicated factoring, look for a greatest common factor. In 6x² + 9x, both terms share 3x, so the expression factors as 3x(2x + 3).

Removing the greatest common factor first often makes the remaining polynomial easier to factor.

Difference of Squares

The pattern a² – b² factors as (a – b)(a + b). For example, x² – 25 = x² – 5² = (x – 5)(x + 5).

This pattern works because multiplying the conjugate factors cancels the middle terms.

Slope and Linear Equations

Slope measures the rate of change of a line. Given two points, slope is the change in y divided by the change in x.

Once the slope is known, a line can be written in slope-intercept form as y = mx + b, where m is slope and b is the y-intercept. The calculator finds b by substituting one of the known points into b = y – mx.

For a more specialized line tool with roof slope, percentage grade, point-slope form, and additional slope modes, use the Slope Calculator.

Undefined Slope

If two points have the same x-coordinate, the run is zero. Division by zero is undefined, so the line has undefined slope. A vertical line is written as x = constant rather than y = mx + b.

Important Algebra Rules

Many algebra errors come from a small set of rules. Remembering these rules makes equation solving much easier.

• Perform the same operation on both sides of an equation.
• Combine only like terms.
• Distribute multiplication across every term inside parentheses.
• Follow the order of operations when evaluating expressions.
• When dividing or multiplying an inequality by a negative number, reverse the inequality sign.
• A denominator cannot equal zero.
• The square root of a negative real number requires complex numbers.
• Check solutions by substituting them back into the original equation.

Order of Operations in Algebra

Algebra uses the same order of operations as arithmetic: grouping symbols first, then exponents, multiplication and division, followed by addition and subtraction. Multiplication and division are handled from left to right, as are addition and subtraction.

For numeric calculations or checking intermediate arithmetic, the Simple Math Calculator is useful alongside the algebra solver.

Exponents in Algebra

An exponent indicates repeated multiplication. x³ means x × x × x. When multiplying powers with the same base, add the exponents: x² × x³ = x⁵. When dividing like bases, subtract exponents when the operation is valid.

A zero exponent gives 1 for any nonzero base. A negative exponent represents a reciprocal: x⁻² = 1/x².

For more advanced powers, roots, logarithms, and scientific functions, the Scientific Calculator is a better fit.

Polynomials

A polynomial is an expression made from constants and variables raised to nonnegative integer powers. x² + 5x + 6 is a quadratic polynomial. 4x³ – 2x + 9 is a cubic polynomial.

The degree of a polynomial is the highest exponent with a nonzero coefficient. Linear polynomials have degree 1, quadratics have degree 2, and cubics have degree 3.

Algebraic Expressions vs Equations

An expression does not contain an equality statement. 3x + 7 is an expression. 3x + 7 = 22 is an equation because it claims that two quantities are equal.

You simplify an expression, but you solve an equation. Keeping that distinction clear helps you choose the right calculator mode.

Variables, Coefficients, and Constants

In 4x + 9, x is the variable, 4 is the coefficient, and 9 is the constant. A coefficient multiplies a variable. If no coefficient is written, the coefficient is understood to be 1, so x means 1x.

Negative variables also have an implied coefficient. -x means -1x.

What Is an Algebra Solver?

An algebra solver is a calculator designed to manipulate expressions or equations rather than only evaluate arithmetic. A basic solver may isolate a variable in a linear equation. More advanced systems can simplify symbolic expressions, solve polynomials, work with inequalities, graph functions, and solve systems.

The calculator here deliberately focuses on common structured problems and explains each method. This avoids the common problem of a simple online calculator appearing to accept any algebra expression but returning an unreliable answer for unsupported input.

Algebra Calculator With Steps

A step-by-step algebra calculator is useful because the intermediate operations often matter more than the final answer. If your result is wrong, seeing the sequence makes it easier to identify whether the mistake came from moving a term, distributing a sign, dividing by a coefficient, or applying a formula incorrectly.

Steps are also valuable for learning. Repeatedly seeing the same operation applied to different numbers helps turn algebraic rules into familiar patterns.

Checking Algebra Answers

Substitution is the standard way to check many algebra answers. Replace the variable in the original equation with the proposed solution and evaluate both sides.

If x = 5 is proposed for 3x + 7 = 22, substitute 5: 3(5) + 7 = 15 + 7 = 22. Because the left side equals the right side, x = 5 checks.

For a system of equations, substitute both x and y into both original equations. A valid ordered pair must satisfy both equations simultaneously.

Worked Algebra Examples

Example 1: Solve 4x + 6 = 30

Subtract 6 from both sides to get 4x = 24. Divide both sides by 4. The solution is x = 6. Checking gives 4(6) + 6 = 30.

Example 2: Solve 7x – 5 = 2x + 20

Move the x terms to one side by subtracting 2x from both sides: 5x – 5 = 20. Add 5 to both sides: 5x = 25. Divide by 5 to get x = 5.

Example 3: Solve x² – 9 = 0

This is a difference of squares: x² – 3² = (x – 3)(x + 3). Set each factor equal to zero. The solutions are x = 3 and x = -3.

Example 4: Simplify 8x + 4 – 3x + 7

Combine the x terms: 8x – 3x = 5x. Combine the constants: 4 + 7 = 11. The simplified expression is 5x + 11.

Example 5: Solve -3x + 4 ≥ 19

Subtract 4 from both sides to get -3x ≥ 15. Divide by -3 and reverse the inequality symbol. The solution is x ≤ -5.

Example 6: Find the Line Through (2, 3) and (6, 11)

Slope is (11 – 3)/(6 – 2) = 8/4 = 2. Use b = y – mx with the first point: b = 3 – 2(2) = -1. The line is y = 2x – 1.

Common Algebra Mistakes

• Changing only one side of an equation.
• Forgetting to distribute a negative sign through parentheses.
• Combining terms that are not like terms.
• Forgetting to reverse an inequality when dividing by a negative number.
• Using the wrong sign for b in the quadratic formula.
• Forgetting the ± symbol when taking a square root in an equation.
• Dividing by zero.
• Stopping before checking whether a solution works in the original equation.
• Rounding too early when a fraction or exact value is available.

Exact Answers vs Decimal Answers

Algebra often prefers exact answers. The fraction 2/3 communicates the exact value, while 0.6667 is an approximation. The calculator attempts to display simple fractional answers when a decimal corresponds closely to a fraction with a reasonable denominator.

Decimals are still useful for measurements, graphing, and practical comparisons. The best form depends on the problem and what the answer will be used for.

When an Equation Has No Solution

A linear equation has no solution when simplifying it produces a false statement with no variable left. For example, x + 2 = x + 5 becomes 2 = 5 after subtracting x from both sides. Since 2 does not equal 5, no value of x can make the original equation true.

When an Equation Has Infinitely Many Solutions

An equation has infinitely many solutions when both sides simplify to the same expression. For example, 2(x + 3) = 2x + 6 simplifies to 2x + 6 = 2x + 6. Every real value of x satisfies the equation.

Algebra and Functions

A function describes how one input is related to an output. The notation f(x) = 2x + 3 means the output is found by multiplying the input x by 2 and adding 3.

Linear functions graph as straight lines. Quadratic functions graph as parabolas. Studying equations and their graphs together is an important bridge between algebra and coordinate geometry.

Algebra and Ratios

Ratios and proportions frequently lead to algebra equations. If 3/5 = x/20, cross multiplication gives 3 × 20 = 5x, so 60 = 5x and x = 12.

For problems focused specifically on proportions and ratio simplification, the Ratio Calculator provides dedicated modes.

Algebra in Everyday Problems

Algebra appears whenever an unknown value must be found from known relationships. A budget equation can solve for how much money remains after fixed costs. A distance problem can solve for time from distance and speed. Construction formulas can solve for an unknown dimension. Business equations can solve for break-even quantity, revenue, or markup.

The letters may change, but the process remains the same: define the unknown, translate the relationship into an equation, isolate the unknown, and check whether the result makes sense.

What This Algebra Calculator Can and Cannot Do

This calculator is built for dependable, common algebra tasks rather than unrestricted symbolic mathematics. It solves structured linear equations, quadratics, two-variable linear systems, linear inequalities, like-term simplification, real quadratic factoring, and two-point line equations.

It does not currently parse arbitrary typed formulas involving logarithms, trigonometry, rational expressions with variables in denominators, matrices larger than 2×2, cubic or quartic symbolic equations, or advanced calculus. A focused calculator that clearly states its limits is more useful than one that silently guesses unsupported input.

How to Rearrange Algebra Formulas

Algebra is often used to solve a formula for a different variable. Instead of finding x in a single numerical equation, the goal is to make one symbol the subject of the formula while leaving the other symbols in place.

Consider the distance formula d = rt, where d is distance, r is rate, and t is time. To solve for time, divide both sides by r to get t = d/r. To solve for rate, divide both sides by t to get r = d/t.

The same balance rules used in ordinary equations still apply. Undo addition and subtraction first when convenient, then multiplication, division, powers, or roots. Rearranging formulas is especially useful in physics, geometry, construction, finance, and engineering.

Standard Form, Point-Slope Form, and Slope-Intercept Form

Linear equations can be written in several equivalent forms. Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Point-slope form is y – y₁ = m(x – x₁), which is convenient when you know one point and the slope. Standard form is commonly written Ax + By = C.

The same line can be converted between these forms. For example, y = 2x – 3 can be rearranged into 2x – y = 3. The form you choose depends on the information given and what you need to find.

OpenStax provides a useful free reference on writing linear equations in slope-intercept, point-slope, and standard form. See Writing Linear Equations from OpenStax Algebra 1 for additional examples.

How to Solve Equations With Variables on Both Sides

Some linear equations place x terms on both sides, such as 7x – 5 = 2x + 20. The usual strategy is to move all variable terms to one side and all constants to the other.

Subtract 2x from both sides to get 5x – 5 = 20. Add 5 to both sides to get 5x = 25. Divide by 5 to get x = 5. You could instead move 7x to the right, but choosing the direction that keeps the variable coefficient positive often makes the arithmetic easier.

If the variable terms cancel completely, inspect the statement that remains. A true statement such as 0 = 0 means infinitely many solutions. A false statement such as 0 = 7 means no solution.

How to Solve Equations With Parentheses

When an equation contains parentheses, the distributive property is often the first step. For example, 3(x + 4) = 21 becomes 3x + 12 = 21. Subtract 12 from both sides to get 3x = 9, then divide by 3 to get x = 3.

Be especially careful when the factor outside the parentheses is negative. -2(x – 5) expands to -2x + 10, not -2x – 10. The negative factor multiplies every term inside the parentheses.

How to Solve Equations With Decimals

Decimal equations can be solved directly, but clearing the decimals may make the work easier. If the equation is 0.4x + 1.2 = 5.6, multiply every term by 10 to get 4x + 12 = 56. Then solve the simpler integer equation.

This works because multiplying every term on both sides by the same nonzero value preserves equality. Choose a power of ten large enough to remove all decimal places.

Absolute Value Equations

An absolute value represents distance from zero, so |x| = 5 has two solutions: x = 5 and x = -5. More generally, an equation such as |2x – 1| = 7 can be split into two equations: 2x – 1 = 7 and 2x – 1 = -7.

The first equation gives x = 4. The second gives x = -3. If an absolute value is set equal to a negative number, there are no real solutions because absolute value cannot be negative.

The current calculator does not have a dedicated absolute-value mode, but understanding this two-case method is useful for Algebra 1 and Algebra 2 problems.

Radicals and Square Roots in Algebra

Radical equations contain square roots or other roots. A common strategy is to isolate the radical and then raise both sides to a power that removes it. For example, √(x + 1) = 5 becomes x + 1 = 25 after squaring both sides, so x = 24.

Squaring both sides can introduce an extraneous solution in more complicated equations, so every proposed answer should be checked in the original equation. A value that makes a denominator zero or produces an invalid radical must be rejected.

Rational Expressions and Restrictions

A rational expression is a fraction whose numerator or denominator contains a polynomial. The most important restriction is that the denominator cannot equal zero.

For an equation such as 1/x = 1/4, x cannot be zero. Cross multiplication gives x = 4, which is valid. In more complicated rational equations, clearing denominators can create candidate solutions that must be checked against the original restrictions.

Function Notation

Function notation writes an output in terms of an input. If f(x) = 3x – 2, then f(5) means substitute 5 for x: f(5) = 3(5) – 2 = 13.

Function notation does not mean f multiplied by x. It names the function and identifies its input. Understanding this notation becomes increasingly important in Algebra 2, precalculus, and calculus.

Domain and Range

The domain of a function is the set of allowed input values. The range is the set of output values the function can produce. For a simple linear function such as y = 2x + 1, both the domain and range are all real numbers.

Restrictions appear in other functions. In y = 1/x, x cannot equal zero. In the real-valued function y = √x, x must be zero or positive. Identifying these restrictions is part of understanding an algebraic formula, not merely evaluating it.

Graphing Algebra Equations

Graphing gives a visual interpretation of an equation. A solution to a one-variable equation can be viewed as a point where two expressions have equal values. A solution to a two-variable system is the intersection of two graphs.

For a linear equation, slope determines how quickly the line rises or falls and the y-intercept identifies where it crosses the vertical axis. For a quadratic, the roots show where the parabola crosses the x-axis and the vertex identifies its turning point.

Graphing is particularly useful for checking whether a numerical solution makes sense. If two lines appear parallel, a claimed intersection point should immediately look suspicious.

The Vertex of a Quadratic

A quadratic function y = ax² + bx + c has a vertex on its axis of symmetry. The x-coordinate of the vertex is -b/(2a). Substituting that x-value back into the function gives the y-coordinate.

If a is positive, the parabola opens upward and the vertex is a minimum. If a is negative, the parabola opens downward and the vertex is a maximum. This information is useful even when the main goal is to solve the roots.

Completing the Square

Completing the square is another method for solving quadratics and rewriting them in vertex form. For x² + 6x + 5, move the constant to get x² + 6x = -5. Add 9 to both sides because half of 6 is 3 and 3² = 9. This gives (x + 3)² = 4.

Taking square roots gives x + 3 = ±2, so x = -1 or x = -5. Completing the square is also the method from which the quadratic formula can be derived.

Factoring by Grouping

Factoring by grouping is useful when a polynomial has four terms. For example, x³ + 3x² + 2x + 6 can be grouped as (x³ + 3x²) + (2x + 6). Factor each group to get x²(x + 3) + 2(x + 3). The shared binomial then gives (x + 3)(x² + 2).

This technique becomes important when factoring higher-degree polynomials and when a common binomial appears after the terms are grouped strategically.

Algebra Word Problems

Word problems are often difficult because the algebra is hidden inside ordinary language. Start by defining the unknown. Then translate each relationship into mathematical symbols before trying to solve anything.

If a gym charges a $25 signup fee plus $30 per month and the total paid is $205, let m be the number of months. The equation is 25 + 30m = 205. Subtract 25 to get 30m = 180, then divide by 30. The membership lasted 6 months.

Units are useful clues. If the unknown is time, the final answer should be in a time unit. If the unknown is money, a negative result may or may not make sense depending on the situation.

Distance, Rate, and Time Problems

The relationship d = rt appears frequently in algebra word problems. If a vehicle travels 180 miles at 60 miles per hour, time is t = d/r = 180/60 = 3 hours.

Problems involving two travelers may require two equations, especially when they move toward each other, away from each other, or start at different times.

Mixture and Percentage Problems

Mixture problems use algebra to combine quantities with different concentrations or prices. A basic setup is amount × concentration = amount of pure substance.

For example, mixing x litres of a 20% solution with 10 litres of a 50% solution to make a 30% solution gives 0.20x + 0.50(10) = 0.30(x + 10). Solving the equation gives the amount of the 20% solution required.

Sequences in Algebra

An arithmetic sequence changes by a constant difference. If a sequence is 5, 8, 11, 14, the common difference is 3. Its nth term can be written aₙ = a₁ + (n – 1)d.

A geometric sequence changes by a constant ratio. If a sequence is 2, 6, 18, 54, the common ratio is 3. Its nth term is aₙ = a₁r^(n – 1).

Why Step-by-Step Algebra Matters

Seeing only the final result can hide whether the method was understood. Step-by-step work shows which property was used, how terms moved, where signs changed, and why an answer follows from the original problem.

This is especially important when studying because two wrong methods can occasionally produce a correct-looking number. A clear sequence of valid operations makes the reasoning visible and easier to verify.

Algebra Calculator Frequently Asked Questions

Final Thoughts

Algebra becomes much easier when each problem is reduced to a sequence of small legal operations. Linear equations rely on balance, quadratics can be analyzed through the discriminant and quadratic formula, systems find values that satisfy multiple equations at once, and inequalities follow many of the same rules with one important sign-reversal exception.

Use the Algebra Calculator to check a result, study the solution steps, and compare your own work with the method shown. The final answer matters, but understanding why each step is allowed is what makes the same algebra skills useful on the next problem.