Linear Equation Solver

Enter Your Linear Equation

Enter your equation in the form: ax + b = c

How to Solve Linear Equations

Basic Steps

Simplify both sides - Combine like terms
Isolate the variable - Get all x terms on one side
Solve for x - Divide by the coefficient
Check your answer - Substitute back into original equation

Types of Linear Equations

One-Step Equations

Example: $x + 5 = 12$

Solution: $x = 7$

Two-Step Equations

Example: $3x - 2 = 10$

Solution: $x = 4$

Multi-Step Equations

Example: $2(x + 3) = 4x - 8$

Solution: $x = 7$

Solved Examples

Example 1: Basic Two-Step

Solve: $2x + 7 = 15$

Step 1: Subtract 7 from both sides

$2x + 7 - 7 = 15 - 7$

$2x = 8$

Step 2: Divide both sides by 2

$x = 4$

Check: $2(4) + 7 = 8 + 7 = 15$ ✓

Example 2: With Fractions

Solve: $\frac{x}{3} - 2 = 5$

Step 1: Add 2 to both sides

$\frac{x}{3} = 7$

Step 2: Multiply both sides by 3

$x = 21$

Check: $\frac{21}{3} - 2 = 7 - 2 = 5$ ✓

Example 3: With Parentheses

Solve: $3(x - 4) = 2x + 1$

Step 1: Distribute

$3x - 12 = 2x + 1$

Step 2: Subtract 2x from both sides

$x - 12 = 1$

Step 3: Add 12 to both sides

$x = 13$

Check: $3(13 - 4) = 3(9) = 27$ and $2(13) + 1 = 27$ ✓

Practice Problems

$x + 8 = 15$
$4x = 28$
$3x - 5 = 16$
$\frac{x}{2} + 3 = 8$
$2(x + 4) = 18$
$5x - 3 = 3x + 7$

Show Answers

$x = 7$
$x = 7$
$x = 7$
$x = 10$
$x = 5$
$x = 5$