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Mathematics · Year 8 · Chapter 1

Keep the balance

Practice

x + 3 = 10: x = 7
x − 4 = 9: x = 13
3x = 21: x = 7
x/2 = 8: x = 16
2x + 1 = 9: x = 4
x + 7 = 7: x = 0
5x = 5: x = 1
4x − 3 = 13: x = 4
The one rule of equations: Do the same thing to BOTH sides
x + 3 = 10 — first move?: Subtract 3 from both sides

Easy questions

x + 5 = 12: x = 7
x − 3 = 4: x = 7
2x = 10: x = 5
x/3 = 4: x = 12
x + 9 = 9: x = 0

Medium questions

2x + 3 = 11: x = 4
3x − 2 = 13: x = 5
5x = 35: x = 7
x/2 + 1 = 6: x = 10
4x + 4 = 4: x = 0

Hard questions

2(x + 3) = 14: x = 4 — divide by 2 first, or expand
3x + 5 = x + 11: x = 3 — subtract x, then 5
10 − x = 4: x = 6
2x − 7 = −1: x = 3
Is x = 13 a solution of x + 3 = 10?: No — 13 + 3 = 16 ≠ 10. Always substitute back.

Lesson

An equation is a set of scales

An equation says two sides weigh the same. x + 3 = 10 means the pans balance. To find x, get it alone — but anything you do to one pan you MUST do to the other, or the equals sign becomes a lie. Subtract 3 from both sides: x = 7. That's all 'moving it over' ever was: subtracting from both sides makes the +3 vanish on the left and appear as −3 on the right. Sam's x = 13 came from moving the 3 without flipping its job. Two habits make equations safe: name the operation you're undoing (+3? then subtract 3 — from both sides), and CHECK by substituting back: 7 + 3 = 10. The check costs five seconds and catches everything.

x + 3 = 10 → subtract 3 both sides → x = 7. Check: 7 + 3 = 10 ✓
3x = 21 → divide both sides by 3 → x = 7.
2x + 1 = 9 → subtract 1 → 2x = 8 → divide by 2 → x = 4.
x/2 = 8 → multiply both sides by 2 → x = 16.

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