Mathematics • Year 7 • Unit 2 • Lesson 14

Two-Step Equations

Build the basics: undo two operations in REVERSE order (SADMEP, Subtract/Add first, then Divide/Multiply) to isolate x.

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 5x − 3 = 22.

Step 1, Identify what's being done to x, in order.

First: × 5 (because 5x means 5 × x). Then: − 3.

Reason: BEDMAS, multiplication happens before subtraction. To UNDO, reverse the order: undo the −3 first, then the ×5. This is SADMEP.

Step 2, Undo the −3 first (add 3 to BOTH sides).

5x − 3 + 3 = 22 + 3 → 5x = 25

Reason: addition undoes subtraction. The +3 cancels the −3 on the left, leaving just 5x. On the right, 22 + 3 = 25.

Step 3, Undo the ×5 (divide BOTH sides by 5).

5x ÷ 5 = 25 ÷ 5 → x = 5

Reason: division undoes multiplication. The ÷5 cancels the ×5 on the left, leaving just x.

Step 4, Check by substitution.

5(5) − 3 = 25 − 3 = 22 ✓ matches the RHS

Answer: x = 5.

Stuck? Revisit lesson § "Reverse Order Undoing", SADMEP: Subtract/Add FIRST, then Divide/Multiply.

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 3x + 4 = 19.

Step 1, Operations on x, in order:

First: × ____, then: + ____ . To undo, reverse: ____________ first, then ____________ .

Step 2, Undo the +4 first (subtract 4 from BOTH sides):

3x + 4 − ____ = 19 − ____ → 3x = ____

Step 3, Undo the ×3 (divide BOTH sides by 3):

3x ÷ ____ = ____ ÷ 3 → x = ____

Step 4, Check:

Substitute: 3(____) + 4 = ____ + 4 = ____ ✓ matches RHS

Stuck? Revisit lesson § "SADMEP", undo + or − first, ×or ÷ second.

3. You do, independent practice

Show your working, at minimum BOTH inverse steps 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 2x + 5 = 17. 1 mark

3.2 Solve 4x − 7 = 5. 1 mark

3.3 Solve 6x − 1 = 23. Check your answer. 1 mark

3.4 What is the FIRST step to solve 5x − 8 = 27? (Don't solve yet, just name the move and write the equation after that move.) 1 mark

Standard, division equations and decimals

3.5 Solve x⁄6 − 3 = 4. (Hint: undo the −3 first, then undo the ÷6.) 2 marks

3.6 Solve 4x + 2.5 = 18.5. 2 marks

Extension, negatives and a fraction answer

3.7 Solve −3x + 11 = 2. (The coefficient is negative.) 2 marks

3.8 Solve 2x + 7 = 12. (Answer is a fraction or decimal.) 2 marks

Stuck on 3.7? Subtract 11 from both sides first → −3x = −9. Then divide both sides by −3.

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 (3x + 4 = 19)

Step 1: × 3 then + 4. To undo, reverse: subtract 4 first, then divide by 3.
Step 2: 3x + 4 − 4 = 19 − 4 → 3x = 15.
Step 3: 3x ÷ 3 = 15 ÷ 3 → x = 5.
Step 4: 3(5) + 4 = 15 + 4 = 19 ✓ matches RHS.

3.1-2x + 5 = 17

Subtract 5: 2x = 12. Divide by 2: x = 6. Check: 2(6) + 5 = 17 ✓.

3.2-4x − 7 = 5

Add 7: 4x = 12. Divide by 4: x = 3. Check: 4(3) − 7 = 5 ✓.

3.3-6x − 1 = 23

Add 1: 6x = 24. Divide by 6: x = 4. Check: 6(4) − 1 = 23 ✓.

3.4, First step for 5x − 8 = 27

Add 8 to BOTH sides. New equation: 5x = 35. (We'd then divide by 5 to get x = 7.)

3.5, x⁄6 − 3 = 4

Add 3 to both sides: x⁄6 = 7. Multiply both sides by 6: x = 42. Check: 42⁄6 − 3 = 7 − 3 = 4 ✓.

3.6-4x + 2.5 = 18.5

Subtract 2.5: 4x = 16. Divide by 4: x = 4. Check: 4(4) + 2.5 = 16 + 2.5 = 18.5 ✓.

3.7, −3x + 11 = 2

Subtract 11: −3x = −9. Divide by −3: x = 3 (negative ÷ negative = positive). Check: −3(3) + 11 = −9 + 11 = 2 ✓.

3.8-2x + 7 = 12

Subtract 7: 2x = 5. Divide by 2: x = 2.5 (or 5⁄2). Check: 2(2.5) + 7 = 5 + 7 = 12 ✓.