Mathematics • Year 7 • Unit 2 • Lesson 12

Solving One-Step Equations (Add/Subtract)

Build the basics: spot the operation acting on x, apply its inverse to BOTH sides, and check your answer by substituting back.

Build · I Do / We Do / You Do

1. I do — fully worked example

Read every line. Each step has a short reason on the right so you can see why, not just what.

Problem. Solve x + 6 = 14.

Step 1 — Identify the operation on x.

x has +6 added to it → inverse is −6

Reason: the opposite of adding is subtracting. To get x by itself, we will take 6 off.

Step 2 — Subtract 6 from BOTH sides.

x + 6 − 6 = 14 − 6

Reason: whatever you do to one side, you do to the other to keep the scales balanced.

Step 3 — Simplify each side.

x = 8

Reason: on the left, +6 − 6 = 0 leaving just x. On the right, 14 − 6 = 8.

Step 4 — Check by substitution.

8 + 6 = 14 ✓ matches the RHS

Answer: x = 8.

Stuck? Revisit lesson § "Solving x + a = b" — undo addition with subtraction.

2. We do — fill in the missing steps

Same structure as Section 1, but with the working faded. Fill in each blank line. 4 marks

Problem. Solve x − 9 = 3.

Step 1 — Operation on x:

x has _______ subtracted from it. Inverse is _______.

Step 2 — Apply the inverse to BOTH sides:

x − 9 + ____ = 3 + ____

Step 3 — Simplify:

x = ____

Step 4 — Check:

Substitute back: ____ − 9 = ____ ✓ matches RHS

Stuck? Revisit lesson § "Solving x − a = b" — undo subtraction with addition.

3. You do — independent practice

Show your working under each question — at minimum, the inverse step on BOTH sides and the final answer. The first four are foundation, the middle two are standard, and the last two are extension.

Foundation — clean whole numbers

3.1 Solve x + 5 = 13. 1 mark

3.2 Solve x − 4 = 10. 1 mark

3.3 Solve x + 9 = 14. Check your answer. 1 mark

3.4 Solve x − 7 = 3. Check your answer. 1 mark

Standard — negatives and the variable on the right

3.5 Solve x + 11 = 7. (The answer is negative — that is fine.) 2 marks

3.6 Solve 5 = x + 12. (Don't be tricked by the variable being on the right — same method, both sides.) 2 marks

Extension — decimals and harder negatives

3.7 Solve x − 3.6 = 8.9. Show every step. 2 marks

3.8 Solve x + 2.5 = −1.5. (The answer is negative and a decimal.) 2 marks

Stuck on 3.8? Same method — subtract 2.5 from both sides. The right side becomes −1.5 − 2.5.

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 (x − 9 = 3)

Step 1: x has 9 subtracted from it; inverse is +9.
Step 2: x − 9 + 9 = 3 + 9.
Step 3: x = 12.
Step 4: Check: 12 − 9 = 3 ✓ matches RHS.

3.1 — x + 5 = 13

Subtract 5 from both sides: x = 13 − 5 = 8. Check: 8 + 5 = 13 ✓.

3.2 — x − 4 = 10

Add 4 to both sides: x = 10 + 4 = 14. Check: 14 − 4 = 10 ✓.

3.3 — x + 9 = 14

Subtract 9 from both sides: x = 14 − 9 = 5. Check: 5 + 9 = 14 ✓.

3.4 — x − 7 = 3

Add 7 to both sides: x = 3 + 7 = 10. Check: 10 − 7 = 3 ✓.

3.5 — x + 11 = 7

Subtract 11 from both sides: x = 7 − 11 = −4. Check: −4 + 11 = 7 ✓.

3.6 — 5 = x + 12

Subtract 12 from both sides: 5 − 12 = x, so x = −7. Check: −7 + 12 = 5 ✓.

3.7 — x − 3.6 = 8.9

Add 3.6 to both sides: x = 8.9 + 3.6 = 12.5. Check: 12.5 − 3.6 = 8.9 ✓.

3.8 — x + 2.5 = −1.5

Subtract 2.5 from both sides: x = −1.5 − 2.5 = −4. Check: −4 + 2.5 = −1.5 ✓.