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 ✓.