∑ Math Academy

Cambridge / IGCSE • Algebra

Solving Linear Equations

Linear equations can be solved by keeping both sides balanced. In this lesson, you will use inverse operations to find an unknown value with confidence.

Learning Objectives

  • Solve one-step and two-step linear equations
  • Use inverse operations accurately
  • Check a solution by substitution

Lesson Explanation

Lesson Content

An equation states that two expressions have the same value. Treat the equals sign as a balance: whatever you do to one side, you must do to the other. Undo addition or subtraction first, then multiplication or division.

💡 Key Takeaway

Take one step at a time, check your working carefully, and keep both sides balanced!

Worked Examples

Example 1

Solve 3x + 5 = 20

  1. Step 1

    Subtract 5 from both sides: 3x = 15

  2. Step 2

    Divide both sides by 3: x = 5

  3. Step 3

    Check: 3(5) + 5 = 20

Example 2

Solve 7 - 2x = 15

  1. Step 1

    Subtract 7 from both sides: -2x = 8

  2. Step 2

    Divide both sides by -2: x = -4

  3. Step 3

    Check: 7 - 2(-4) = 15

Visual Method

Balance Every Step

Mathematics becomes much clearer when you can see the structure behind equations.

Watch Video Explanation

Practice Questions

Try solving each question on paper first. Tap below to check a helpful hint or solution!

Question 1

4x - 7 = 21

Show Hint / Solution 💡

Add 7 to both sides first, then divide by 4.

Question 2

5 + 3x = 26

Show Hint / Solution 💡

Subtract 5 from both sides first, then divide by 3.

Question 3

18 - 3x = 6

Show Hint / Solution 💡

Subtract 18 from both sides, then divide by -3.

Lesson Summary

What to Remember

Use inverse operations in reverse order, keep an equation balanced, and substitute your answer back in to check it.

Download Lesson Notes ↓