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Linear equations: collect like terms

Collect variable terms on the same side, handle negative coefficients and check each solution. A 40-minute projection and paper lesson.

40 minutes · Year 7, upper volume · text pp. 59–60 · foundation lesson 30

Textbook reference: Year 7, upper volume · Chapter 3 §3.2

One worked example, one guided attempt, eight core questions, four follow-ups and two extensions. Write on paper; the teacher controls the reveal.

Teacher referenceArrange in My Classroom

  1. 4′Check prerequisites
  2. 5′Observe and predict
  3. 8′Worked example and guided attempt
  4. 15′Independent practice
  5. 5′Discuss and correct
  6. 3′Exit questions

Observe · explain

A question before practising

Project 3x − 5x = 10. Ask for the combined coefficient before solving. Compare 3 − 5 with 5 − 3 and test the two proposed solutions in the original equation.

Organise the key idea

For like terms, add their signed coefficients and keep the variable. After collecting terms, divide both sides by the nonzero coefficient.

Open the original chapterOpen the interactive inquiry

Use the lesson question here for paper discussion; the original activity opens separately.

Worked example1

Solve 3x + 2x = 25. Explain what is added when like terms are collected.

3x+2x=253x+2x=25
Check your work
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Guided attempt2

Solve 7x − 3x + 6 = 22. Complete the three lines on paper before checking.

7x−3x+6=227x-3x+6=22
  1. 7x − 3x = ____ x, so ____ x + 6 = 22.
  2. Subtract 6 from both sides: ____ x = ____.
  3. Divide both sides by ____: x = ____. Then substitute.
Check your work
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Prerequisite3

Complete 3x − 5x = ____ x. Write only the coefficient.

3x−5x=‾x3x-5x=\underline{\qquad}x
Check your work
  • Identify −5 as the second signed coefficient.
  • Give −2 and retain the variable in the completed expression.
Prerequisite4

For −4x = 20, what should both sides be divided by to make the coefficient of x equal to 1? State the solution and check it.

−4x=20-4x=20
Check your work
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Independent practice5

Solve 4x + 3x = 42.

4x+3x=424x+3x=42
Check your work
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Independent practice6

Solve 9x − 5x − 3 = 13.

9x−5x−3=139x-5x-3=13
Check your work
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Independent practice7

Solve 2x − 7x = 30.

2x−7x=302x-7x=30
Check your work
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Independent practice8

Solve −6x + x + 8 = −12.

−6x+x+8=−12-6x+x+8=-12
Check your work
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Exit question9

Solve −3x − 2x = 15. Include a substitution check.

−3x−2x=15-3x-2x=15
Check your work
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Exit question10

For 4x − 7x = 18, a learner writes 3x = 18 and x = 6. Identify the first error, correct the solution and check it.

4x−7x=184x-7x=18
Check your work
  • Locate the error at 4x − 7x = 3x.
  • Correct to −3x and x = −6, with a valid substitution check.
Further practice11

Solve 8x − 2x = −24.

8x−2x=−248x-2x=-24
Check your work
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Further practice12

Solve 5x − 9x + 7 = 27.

5x−9x+7=275x-9x+7=27
Check your work
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Further practice13

Solve −2x − 5x − 9 = 12.

−2x−5x−9=12-2x-5x-9=12
Check your work
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Further practice14

Solve 10x − 6x + 3x = −14.

10x−6x+3x=−1410x-6x+3x=-14
Check your work
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Extension15

Solve 12x − 8x − 3x − 9 = 0. Explain why x remains after collecting the variable terms.

12x−8x−3x−9=012x-8x-3x-9=0
Check your work
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Extension16

Solve −2x − 4x + 3x + 17 = −1. Check without changing the original order of the terms.

−2x−4x+3x+17=−1-2x-4x+3x+17=-1
Check your work
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Preparation and assessment notes

Prerequisites

Signed-number addition, the meaning of a coefficient, like terms and the equality rules.

Look for in students’ work

Keep the signs attached to the terms. Use the guided scaffold before independent work; ask learners to show the collected equation and a substitution check on paper. Brackets, denominator clearing and systems are outside this lesson.

Collect the paper exit questions and note completion and common errors. This page does not grade or store paper answers.

Paper for the class

Download all worksheets (ZIP · 318 PDFs · 47.2 MB)

All 53 Year 7–8 upper- and lower-volume packs in Traditional Chinese and English. Includes teacher answers; student core, further practice and teacher papers are in separate folders.

Core student worksheet: two A4 pages. Further practice is separate. Teacher copies include reference reasoning.

Textbook reference and authorship

Original practice aligned to the referenced skills. Use your own textbook for the cited pages.

大湾区初中数学三维课堂（七年级上册）正文.pdf

Year 7, upper volume · text pp. 59–60 · foundation lesson 30

Original questions and explanations; the source textbook and answer PDFs are not reproduced here.

Linear equations: collect like terms

Year 7, upper volume · text pp. 59–60 · foundation lesson 30 · 1/2

Name: __________ Class: ______ Date: __________

Worked example1

Solve 3x + 2x = 25. Explain what is added when like terms are collected.

3x+2x=253x+2x=25
Guided attempt2

Solve 7x − 3x + 6 = 22. Complete the three lines on paper before checking.

7x−3x+6=227x-3x+6=22
  1. 7x − 3x = ____ x, so ____ x + 6 = 22.
  2. Subtract 6 from both sides: ____ x = ____.
  3. Divide both sides by ____: x = ____. Then substitute.
Prerequisite3

Complete 3x − 5x = ____ x. Write only the coefficient.

3x−5x=‾x3x-5x=\underline{\qquad}x
Prerequisite4

For −4x = 20, what should both sides be divided by to make the coefficient of x equal to 1? State the solution and check it.

−4x=20-4x=20
g7-equations-collect · 2026-10-14-guided-practice-v1 · Conditions and reasons matter; measurement is not proof.

Linear equations: collect like terms

Year 7, upper volume · text pp. 59–60 · foundation lesson 30 · 2/2

Name: __________ Class: ______ Date: __________

Independent practice5

Solve 4x + 3x = 42.

4x+3x=424x+3x=42
Independent practice6

Solve 9x − 5x − 3 = 13.

9x−5x−3=139x-5x-3=13
Independent practice7

Solve 2x − 7x = 30.

2x−7x=302x-7x=30
Independent practice8

Solve −6x + x + 8 = −12.

−6x+x+8=−12-6x+x+8=-12
Exit question9

Solve −3x − 2x = 15. Include a substitution check.

−3x−2x=15-3x-2x=15
Exit question10

For 4x − 7x = 18, a learner writes 3x = 18 and x = 6. Identify the first error, correct the solution and check it.

4x−7x=184x-7x=18
g7-equations-collect · 2026-10-14-guided-practice-v1 · Conditions and reasons matter; measurement is not proof.

Linear equations: collect like terms — Further practice

Year 7, upper volume · text pp. 59–60 · foundation lesson 30

Further practice11

Solve 8x − 2x = −24.

8x−2x=−248x-2x=-24
Further practice12

Solve 5x − 9x + 7 = 27.

5x−9x+7=275x-9x+7=27
Further practice13

Solve −2x − 5x − 9 = 12.

−2x−5x−9=12-2x-5x-9=12
Further practice14

Solve 10x − 6x + 3x = −14.

10x−6x+3x=−1410x-6x+3x=-14
Extension15

Solve 12x − 8x − 3x − 9 = 0. Explain why x remains after collecting the variable terms.

12x−8x−3x−9=012x-8x-3x-9=0
Extension16

Solve −2x − 4x + 3x + 17 = −1. Check without changing the original order of the terms.

−2x−4x+3x+17=−1-2x-4x+3x+17=-1

Linear equations: collect like terms — Teacher answers

Year 7, upper volume · text pp. 59–60 · foundation lesson 30

Keep the signs attached to the terms. Use the guided scaffold before independent work; ask learners to show the collected equation and a substitution check on paper. Brackets, denominator clearing and systems are outside this lesson.

Worked example1

Solve 3x + 2x = 25. Explain what is added when like terms are collected.

3x+2x=253x+2x=25
Reference answer

x = 5.

  1. The terms are like terms: 3x + 2x = 5x. The coefficients are added.
  2. The equation becomes 5x = 25. Divide both sides by 5 to get x = 5.
  3. Check: 3 × 5 + 2 × 5 = 15 + 10 = 25.
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Guided attempt2

Solve 7x − 3x + 6 = 22. Complete the three lines on paper before checking.

7x−3x+6=227x-3x+6=22
  1. 7x − 3x = ____ x, so ____ x + 6 = 22.
  2. Subtract 6 from both sides: ____ x = ____.
  3. Divide both sides by ____: x = ____. Then substitute.
Reference answer

x = 4.

  1. Collect the variable terms: 7x − 3x = 4x, so 4x + 6 = 22.
  2. Subtract 6 from both sides: 4x = 16. Divide both sides by 4: x = 4.
  3. Check: 7 × 4 − 3 × 4 + 6 = 28 − 12 + 6 = 22.
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Prerequisite3

Complete 3x − 5x = ____ x. Write only the coefficient.

3x−5x=‾x3x-5x=\underline{\qquad}x
Reference answer

The coefficient is −2: 3x − 5x = −2x.

  1. The signed coefficients are 3 and −5.
  2. 3 + (−5) = −2; keep x.
  • Identify −5 as the second signed coefficient.
  • Give −2 and retain the variable in the completed expression.
Prerequisite4

For −4x = 20, what should both sides be divided by to make the coefficient of x equal to 1? State the solution and check it.

−4x=20-4x=20
Reference answer

Divide both sides by −4, not 4. Then x = −5 and −4 × (−5) = 20.

  1. Divide both sides by −4: x = −5.
  2. Check: −4 × (−5) = 20.
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Independent practice5

Solve 4x + 3x = 42.

4x+3x=424x+3x=42
Reference answer

x = 6.

  1. Collect like terms: 7x = 42.
  2. Divide both sides by 7: x = 6.
  3. Check: 4 × 6 + 3 × 6 = 42.
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Independent practice6

Solve 9x − 5x − 3 = 13.

9x−5x−3=139x-5x-3=13
Reference answer

x = 4.

  1. Collect the variable terms: 4x − 3 = 13.
  2. Add 3 to both sides: 4x = 16. Divide by 4: x = 4.
  3. Check: 9 × 4 − 5 × 4 − 3 = 13.
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Independent practice7

Solve 2x − 7x = 30.

2x−7x=302x-7x=30
Reference answer

x = -6.

  1. 2 − 7 = −5, so −5x = 30.
  2. Divide both sides by −5: x = −6.
  3. Check: 2 × (−6) − 7 × (−6) = −12 + 42 = 30.
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Independent practice8

Solve −6x + x + 8 = −12.

−6x+x+8=−12-6x+x+8=-12
Reference answer

x = 4.

  1. The coefficient of x alone is 1: −6x + x = −5x.
  2. −5x + 8 = −12. Subtract 8: −5x = −20. Divide by −5: x = 4.
  3. Check: −6 × 4 + 4 + 8 = −12.
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Exit question9

Solve −3x − 2x = 15. Include a substitution check.

−3x−2x=15-3x-2x=15
Reference answer

x = -3.

  1. −3x − 2x = −5x, so −5x = 15.
  2. Divide both sides by −5: x = −3.
  3. Check: −3 × (−3) − 2 × (−3) = 9 + 6 = 15.
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Exit question10

For 4x − 7x = 18, a learner writes 3x = 18 and x = 6. Identify the first error, correct the solution and check it.

4x−7x=184x-7x=18
Reference answer

4 − 7 = −3, not 3. Thus −3x = 18 and x = −6. Substitution gives −24 + 42 = 18.

  1. The first error is losing the sign when calculating 4 − 7.
  2. Correct it to −3x = 18, then divide both sides by −3: x = −6.
  3. Check the original equation: 4 × (−6) − 7 × (−6) = 18.
  • Locate the error at 4x − 7x = 3x.
  • Correct to −3x and x = −6, with a valid substitution check.
Further practice11

Solve 8x − 2x = −24.

8x−2x=−248x-2x=-24
Reference answer

x = -4.

  1. Collect: 6x = −24.
  2. Divide both sides by 6: x = −4.
  3. Check: 8 × (−4) − 2 × (−4) = −24.
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Further practice12

Solve 5x − 9x + 7 = 27.

5x−9x+7=275x-9x+7=27
Reference answer

x = -5.

  1. Collect: −4x + 7 = 27.
  2. Subtract 7: −4x = 20. Divide by −4: x = −5.
  3. Check: 5 × (−5) − 9 × (−5) + 7 = 27.
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Further practice13

Solve −2x − 5x − 9 = 12.

−2x−5x−9=12-2x-5x-9=12
Reference answer

x = -3.

  1. Collect: −7x − 9 = 12.
  2. Add 9: −7x = 21. Divide by −7: x = −3.
  3. Check: −2 × (−3) − 5 × (−3) − 9 = 12.
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Further practice14

Solve 10x − 6x + 3x = −14.

10x−6x+3x=−1410x-6x+3x=-14
Reference answer

x = -2.

  1. 10 − 6 + 3 = 7, so 7x = −14.
  2. Divide both sides by 7: x = −2.
  3. Check: 10 × (−2) − 6 × (−2) + 3 × (−2) = −14.
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Extension15

Solve 12x − 8x − 3x − 9 = 0. Explain why x remains after collecting the variable terms.

12x−8x−3x−9=012x-8x-3x-9=0
Reference answer

x = 9.

  1. 12 − 8 − 3 = 1, so the variable terms combine to 1x = x.
  2. x − 9 = 0. Add 9 to both sides: x = 9.
  3. Check: 12 × 9 − 8 × 9 − 3 × 9 − 9 = 0.
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.
Extension16

Solve −2x − 4x + 3x + 17 = −1. Check without changing the original order of the terms.

−2x−4x+3x+17=−1-2x-4x+3x+17=-1
Reference answer

x = 6.

  1. −2 − 4 + 3 = −3, so −3x + 17 = −1.
  2. Subtract 17: −3x = −18. Divide by −3: x = 6.
  3. Check: −2 × 6 − 4 × 6 + 3 × 6 + 17 = −12 − 24 + 18 + 17 = −1.
  • Combine only like terms and keep both sides equal.
  • Find the stated value and check it in the original equation.