What is a Linear Equation?

A linear equation has an unknown variable (usually x) and no exponents higher than 1. Solving it means finding the value of x that makes the equation true.

The Golden Rule: Whatever you do to one side, do to the other!

Think of a Balance Scale

An equation is like a balanced scale. To keep it balanced, every operation you do on the left must also be done on the right.

Left Side

x + 5

=

Right Side

12

One-Step Equations

These need just one operation to isolate x. Use the inverse (opposite) operation.

x + 7 = 15

Subtract 7 from both sides:

x = 15 − 7 = 8

3x = 18

Divide both sides by 3:

x = 18 ÷ 3 = 6

Two-Step Equations

These need two operations. Always undo addition/subtraction first, then multiplication/division.

1

Solve: 2x + 5 = 17

Step 1: Subtract 5: 2x = 17 − 5 = 12

Step 2: Divide by 2: x = 12 ÷ 2 = 6

Check: 2(6) + 5 = 12 + 5 = 17 ✓

2

Solve: 4x − 3 = 21

Step 1: Add 3: 4x = 21 + 3 = 24

Step 2: Divide by 4: x = 24 ÷ 4 = 6

Check: 4(6) − 3 = 24 − 3 = 21 ✓

Checking Your Solution

Always substitute your answer back into the original equation to verify it works. If both sides are equal, your answer is correct!

Pro tip: Checking only takes a few seconds and can save you from careless mistakes. Make it a habit!

Knowledge Check

Select the correct answer for each question. Questions get harder as you go!

Question 1

Solve: x + 9 = 14

x = 23 x = 9 x = 5 x = 4

Question 2

Solve: 5x = 35

x = 30 x = 175 x = 40 x = 7

Question 3

Solve: x − 8 = 3

x = 11 x = 5 x = −5 x = 24

Question 4

Solve: 3x + 4 = 19

x = 7 x = 5 x = 15 x = 23

Question 5

Solve: 2x − 7 = 11

x = 2 x = 4 x = 9 x = 18

Question 6

Solve: x/4 + 3 = 8

x = 44 x = 32 x = 5 x = 20

Question 7

Is x = 4 a solution to 3x + 2 = 15?

No Yes Not enough information Only if x is positive

Question 8

Solve: 5x + 3 = 2x + 18

x = 3 x = 5 x = 7 x = 15

Question 9

Solve: 4(x − 2) = 20

x = 3 x = 22 x = 7 x = 6

Question 10

Solve: 3(2x + 1) − 4 = 2(x + 5) + 1

x = 2 x = 4 x = 2.5 x = 3

Linear Equations