Mathematics • Year 8 • Unit 2 • Lesson 16

Solving Linear Equations Review

Re-train the balance method with inverse operations. One fully worked two-step equation, one guided example with blanks, then eight graduated problems from one-step through brackets and unknowns on both sides.

Build · I Do / We Do / You Do

1. I do — fully worked example

Read every line. Each step says why, not just what. The big rule: do the same operation to both sides, and undo addition/subtraction before multiplication/division (reverse BODMAS).

Problem. Solve 3x + 4 = 16.

Step 1 — Identify the operations done to x.

x has been multiplied by 3, then 4 was added.

Reason: to isolate x we undo these in reverse order — undo the +4 first.

Step 2 — Subtract 4 from BOTH sides (undo +4).

3x + 4 − 4 = 16 − 4

3x = 12

Reason: same op both sides keeps the equation balanced.

Step 3 — Divide both sides by 3 (undo ×3).

3x ÷ 3 = 12 ÷ 3

x = 4

Step 4 — Check by substituting x = 4 back into the original.

LHS = 3(4) + 4 = 12 + 4 = 16 = RHS ✓

Answer: x = 4.

Stuck? Revisit lesson § "Two-Step Equations". Reverse BODMAS: undo +/− first, then ×/÷.

2. We do — fill in the missing steps

Same shape as Section 1, but with blanks. Fill every blank in pencil. 5 marks

Problem. Solve 2x − 5 = 9.

Step 1 — Operations done to x: x has been multiplied by ______, then ______ was subtracted.

Step 2 — Undo the −5: ______ ______ to both sides.

2x − 5 + ______ = 9 + ______

2x = ______

Step 3 — Undo the ×2: ______ both sides by ______.

x = ______

Step 4 — Check: LHS = 2(______) − 5 = ______ − 5 = ______. RHS = 9. ______ ≟ ______.

Answer: x = ______.

Stuck? The inverse of "−5" is "+5". The inverse of "×2" is "÷2".

3. You do — independent practice

Show every step. 3.1–3.3 are foundation (one-step). 3.4–3.6 are standard (two-step and brackets). 3.7–3.8 are extension (unknowns on both sides / fractions).

Foundation — one-step equations

3.1 Solve x + 9 = 15. 1 mark

3.2 Solve x − 7 = 12. 1 mark

3.3 Solve 4x = 28. 1 mark

Standard — two-step and brackets

3.4 Solve 5x + 3 = 23. Show both inverse operations. 2 marks

3.5 Solve x/3 + 2 = 9. Remember reverse BODMAS! 2 marks

3.6 Solve 4(x − 1) = 20. Expand the brackets first. 2 marks

Extension — unknowns on both sides

3.7 Solve 5x − 3 = 2x + 12. Move the smaller x term first. 3 marks

3.8 Solve 3(x − 1) = 2(x + 4). Expand both sides first, then collect. 3 marks

Stuck on 3.7? Subtract 2x from both sides FIRST so the x stays positive.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

Section 2 — We do 2x − 5 = 9

Step 1: multiplied by 2, then 5 subtracted.
Step 2: Add 5 to both sides: 2x − 5 + 5 = 9 + 5 → 2x = 14.
Step 3: Divide both sides by 2: x = 7.
Step 4: LHS = 2(7) − 5 = 14 − 5 = 9. RHS = 9. 9 = 9 ✓.
Answer: x = 7.

3.1 — x + 9 = 15

Subtract 9 from both sides: x = 6. Check: 6 + 9 = 15 ✓.

3.2 — x − 7 = 12

Add 7 to both sides: x = 19. Check: 19 − 7 = 12 ✓.

3.3 — 4x = 28

Divide both sides by 4: x = 7. Check: 4(7) = 28 ✓.

3.4 — 5x + 3 = 23

Subtract 3: 5x = 20. Divide by 5: x = 4. Check: 5(4) + 3 = 23 ✓.

3.5 — x/3 + 2 = 9

Subtract 2 first (reverse BODMAS): x/3 = 7. Multiply both sides by 3: x = 21. Check: 21/3 + 2 = 7 + 2 = 9 ✓.

3.6 — 4(x − 1) = 20

Expand: 4x − 4 = 20. Add 4: 4x = 24. Divide by 4: x = 6. Check: 4(6 − 1) = 4(5) = 20 ✓.

3.7 — 5x − 3 = 2x + 12

Subtract 2x (the smaller term): 3x − 3 = 12. Add 3: 3x = 15. Divide by 3: x = 5. Check: LHS = 5(5) − 3 = 22; RHS = 2(5) + 12 = 22 ✓.

3.8 — 3(x − 1) = 2(x + 4)

Expand both: 3x − 3 = 2x + 8. Subtract 2x: x − 3 = 8. Add 3: x = 11. Check: LHS = 3(10) = 30; RHS = 2(15) = 30 ✓.