Then the equation is no longer linear in x. 0 = c − b has infinite solutions if b = c, none otherwise.

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Linear Equation Solver — Step by Step (Free)

Free linear equation solver with full working. Type ax + b = c — see the solution in four steps with verification and notes. Grade 7 algebra, no signup.

Quick answer

How do you solve a linear equation?

A linear equation of the form ax + b = c is solved in two moves: first subtract b from both sides, then divide by a. The result is x = (c − b) ÷ a. Always verify by substituting back into the original equation.

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3 + boss question

HowTo

Solve a linear equation — in 4 steps

Walkthrough using 3x + 7 = 22

1
Step 1 of 4
Write the equation
Write it down clearly: 3x + 7 = 22. Identify a = 3, b = 7, c = 22.
2
Step 2 of 4
Isolate the constant
Subtract 7 from both sides. You get 3x = 22 − 7, so 3x = 15.
3
Step 3 of 4
Divide by the coefficient
Divide both sides by 3. The result is x = 15 ÷ 3 = 5.
4
Step 4 of 4
Verify
Substitute x = 5 back: 3·5 + 7 = 15 + 7 = 22 ✓.

Examples

Worked examples

Typical problem types with full working

2x − 5 = 9

+ 5: 2x = 14

÷ 2: x = 7

x = 7

−4x + 12 = 0

− 12: −4x = −12

÷ (−4): x = 3

x = 3

5x + 3 = 18

− 3: 5x = 15

÷ 5: x = 3

x = 3

Theory

What is a linear equation?

A linear equation is an equation in one variable where the variable appears only to the first power. Its general form is ax + b = c, with a, b, c real numbers and a ≠ 0. Exactly one solution x exists whenever a ≠ 0. Linear equations show up in algebra from Grade 7 onwards — and everywhere two quantities scale proportionally: pricing, speed, mixing ratios.

Pitfalls

Common mistakes

Forgetting sign flips

When you subtract on both sides, signs change — +7 becomes −7. Write the operation out explicitly.

Dividing by a negative

For equations, nothing else changes. For inequalities, the comparison sign would flip.

Skipping the check

Always plug your solution back in.

FAQ

Frequently asked

How do I solve 3x + 7 = 22?

Subtract 7: 3x = 15. Divide by 3: x = 5. Check: 3·5 + 7 = 22 ✓.

What is the general formula for ax + b = c?

What if a = 0?

How do I solve with x on both sides?

Does the calculator work with fractions or decimals?

When are linear equations taught?

Glossary

Quick definitions

Variable: A placeholder for an unknown number, typically x.
Coefficient: The number multiplying the variable. In 3x, 3 is the coefficient.
Constant: A standalone number. In 3x + 7, 7 is the constant.
Linear equation: Equation of the form ax + b = c with a ≠ 0.
Solution: The value of x that makes the equation true.
Verification: Substituting the found solution back into the original equation to confirm.