PAPER · REASONING · PRACTICE

Linear equations: collect like terms — Teacher reference

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.

Student classroom page Arrange in My Classroom

Lesson routePhase

4′Check prerequisites
5′Observe and predict
8′Worked example and guided attempt
15′Independent practice
5′Discuss and correct
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 chapter Open 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=25

Compare the variables in the two terms.
Add 3 and 2; keep x.
After collecting, solve 5x = 25.

The terms are like terms: 3x + 2x = 5x. The coefficients are added.
The equation becomes 5x = 25. Divide both sides by 5 to get x = 5.
Check: 3 × 5 + 2 × 5 = 15 + 10 = 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=22

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

Collect 7x and −3x; leave the constant 6 separate.
Use the signed coefficients: 7 − 3 = 4.
Solve 4x + 6 = 22 by subtracting 6, then dividing by 4.

Collect the variable terms: 7x − 3x = 4x, so 4x + 6 = 22.
Subtract 6 from both sides: 4x = 16. Divide both sides by 4: x = 4.
Check: 7 × 4 − 3 × 4 + 6 = 28 − 12 + 6 = 22.

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=\underline{\qquad}x

Keep the minus sign with 5x.
The coefficient calculation is 3 − 5.
The difference is negative because 5 is larger than 3.

The signed coefficients are 3 and −5.
3 + (−5) = −2; keep 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

The coefficient of x is −4, not 4.
Divide both sides by the whole signed coefficient.
A positive number divided by a negative number is negative.

Divide both sides by −4: x = −5.
Check: −4 × (−5) = 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=42

The two terms have the same variable.
Add the coefficients 4 and 3.
Solve 7x = 42.

Collect like terms: 7x = 42.
Divide both sides by 7: x = 6.
Check: 4 × 6 + 3 × 6 = 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=13

Do not combine the constant −3 with the x terms.
9x − 5x = 4x.
Remove −3 by adding 3 to both sides.

Collect the variable terms: 4x − 3 = 13.
Add 3 to both sides: 4x = 16. Divide by 4: x = 4.
Check: 9 × 4 − 5 × 4 − 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=30

Keep the order 2 − 7.
The combined coefficient is −5.
Divide 30 by −5.

2 − 7 = −5, so −5x = 30.
Divide both sides by −5: x = −6.
Check: 2 × (−6) − 7 × (−6) = −12 + 42 = 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

Write x as 1x before collecting.
−6 + 1 = −5.
After collecting, subtract 8 from both sides.

The coefficient of x alone is 1: −6x + x = −5x.
−5x + 8 = −12. Subtract 8: −5x = −20. Divide by −5: x = 4.
Check: −6 × 4 + 4 + 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

Both signed coefficients are negative.
Add −3 and −2.
Divide 15 by the combined coefficient −5.

−3x − 2x = −5x, so −5x = 15.
Divide both sides by −5: x = −3.
Check: −3 × (−3) − 2 × (−3) = 9 + 6 = 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=18

Check the line before x = 6.
Is 4 − 7 positive or negative?
Use −3 as the coefficient and test the resulting solution.

The first error is losing the sign when calculating 4 − 7.
Correct it to −3x = 18, then divide both sides by −3: x = −6.
Check the original equation: 4 × (−6) − 7 × (−6) = 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=-24

Subtract the signed coefficients.
8 − 2 = 6.
A negative number divided by 6 remains negative.

Collect: 6x = −24.
Divide both sides by 6: x = −4.
Check: 8 × (−4) − 2 × (−4) = −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=27

Combine the x terms, keeping their signs.
5 − 9 = −4.
First remove +7, then divide by −4.

Collect: −4x + 7 = 27.
Subtract 7: −4x = 20. Divide by −4: x = −5.
Check: 5 × (−5) − 9 × (−5) + 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

The coefficients are −2 and −5.
Their sum is −7.
Add 9 to both sides before dividing.

Collect: −7x − 9 = 12.
Add 9: −7x = 21. Divide by −7: x = −3.
Check: −2 × (−3) − 5 × (−3) − 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=-14

All three variable terms are like terms.
Calculate 10 − 6 + 3 in order.
Solve 7x = −14.

10 − 6 + 3 = 7, so 7x = −14.
Divide both sides by 7: x = −2.
Check: 10 × (−2) − 6 × (−2) + 3 × (−2) = −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=0

Do not omit the coefficient of −3x.
Compute 12 − 8 − 3, not 12 − 8 + 3.
The coefficient is 1; now solve x − 9 = 0.

12 − 8 − 3 = 1, so the variable terms combine to 1x = x.
x − 9 = 0. Add 9 to both sides: x = 9.
Check: 12 × 9 − 8 × 9 − 3 × 9 − 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

There are three signed variable coefficients.
Combine −2, −4 and +3.
After subtracting 17, both sides are negative.

−2 − 4 + 3 = −3, so −3x + 17 = −1.
Subtract 17: −3x = −18. Divide by −3: x = 6.
Check: −2 × 6 − 4 × 6 + 3 × 6 + 17 = −12 − 24 + 18 + 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.

All reference answers

Worked example1

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

3x+2x=25

Reference answer

x = 5.

The terms are like terms: 3x + 2x = 5x. The coefficients are added.
The equation becomes 5x = 25. Divide both sides by 5 to get x = 5.
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=22

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

Reference answer

x = 4.

Collect the variable terms: 7x − 3x = 4x, so 4x + 6 = 22.
Subtract 6 from both sides: 4x = 16. Divide both sides by 4: x = 4.
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=\underline{\qquad}x

Reference answer

The coefficient is −2: 3x − 5x = −2x.

The signed coefficients are 3 and −5.
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

Reference answer

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

Divide both sides by −4: x = −5.
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=42

Reference answer

x = 6.

Collect like terms: 7x = 42.
Divide both sides by 7: x = 6.
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=13

Reference answer

x = 4.

Collect the variable terms: 4x − 3 = 13.
Add 3 to both sides: 4x = 16. Divide by 4: x = 4.
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=30

Reference answer

x = -6.

2 − 7 = −5, so −5x = 30.
Divide both sides by −5: x = −6.
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

Reference answer

x = 4.

The coefficient of x alone is 1: −6x + x = −5x.
−5x + 8 = −12. Subtract 8: −5x = −20. Divide by −5: x = 4.
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

Reference answer

x = -3.

−3x − 2x = −5x, so −5x = 15.
Divide both sides by −5: x = −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=18

Reference answer

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

The first error is losing the sign when calculating 4 − 7.
Correct it to −3x = 18, then divide both sides by −3: x = −6.
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=-24

Reference answer

x = -4.

Collect: 6x = −24.
Divide both sides by 6: x = −4.
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=27

Reference answer

x = -5.

Collect: −4x + 7 = 27.
Subtract 7: −4x = 20. Divide by −4: x = −5.
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

Reference answer

x = -3.

Collect: −7x − 9 = 12.
Add 9: −7x = 21. Divide by −7: x = −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=-14

Reference answer

x = -2.

10 − 6 + 3 = 7, so 7x = −14.
Divide both sides by 7: x = −2.
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=0

Reference answer

x = 9.

12 − 8 − 3 = 1, so the variable terms combine to 1x = x.
x − 9 = 0. Add 9 to both sides: x = 9.
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

Reference answer

x = 6.

−2 − 4 + 3 = −3, so −3x + 17 = −1.
Subtract 17: −3x = −18. Divide by −3: x = 6.
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.

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.

Print edition

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=25

Guided attempt2

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

7x-3x+6=22

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

Prerequisite3

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

3x-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

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=42

Independent practice6

Solve 9x − 5x − 3 = 13.

9x-5x-3=13

Independent practice7

Solve 2x − 7x = 30.

2x-7x=30

Independent practice8

Solve −6x + x + 8 = −12.

-6x+x+8=-12

Exit question9

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

-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=18

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=-24

Further practice12

Solve 5x − 9x + 7 = 27.

5x-9x+7=27

Further practice13

Solve −2x − 5x − 9 = 12.

-2x-5x-9=12

Further practice14

Solve 10x − 6x + 3x = −14.

10x-6x+3x=-14

Extension15

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

12x-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

Linear equations: collect like terms — Teacher answers

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

Worked example1

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

3x+2x=25

Reference answer

x = 5.

The terms are like terms: 3x + 2x = 5x. The coefficients are added.
The equation becomes 5x = 25. Divide both sides by 5 to get x = 5.
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=22

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

Reference answer

x = 4.

Collect the variable terms: 7x − 3x = 4x, so 4x + 6 = 22.
Subtract 6 from both sides: 4x = 16. Divide both sides by 4: x = 4.
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=\underline{\qquad}x

Reference answer

The coefficient is −2: 3x − 5x = −2x.

The signed coefficients are 3 and −5.
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

Reference answer

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

Divide both sides by −4: x = −5.
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=42

Reference answer

x = 6.

Collect like terms: 7x = 42.
Divide both sides by 7: x = 6.
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=13

Reference answer

x = 4.

Collect the variable terms: 4x − 3 = 13.
Add 3 to both sides: 4x = 16. Divide by 4: x = 4.
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=30

Reference answer

x = -6.

2 − 7 = −5, so −5x = 30.
Divide both sides by −5: x = −6.
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

Reference answer

x = 4.

The coefficient of x alone is 1: −6x + x = −5x.
−5x + 8 = −12. Subtract 8: −5x = −20. Divide by −5: x = 4.
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

Reference answer

x = -3.

−3x − 2x = −5x, so −5x = 15.
Divide both sides by −5: x = −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=18

Reference answer

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

The first error is losing the sign when calculating 4 − 7.
Correct it to −3x = 18, then divide both sides by −3: x = −6.
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=-24

Reference answer

x = -4.

Collect: 6x = −24.
Divide both sides by 6: x = −4.
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=27

Reference answer

x = -5.

Collect: −4x + 7 = 27.
Subtract 7: −4x = 20. Divide by −4: x = −5.
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

Reference answer

x = -3.

Collect: −7x − 9 = 12.
Add 9: −7x = 21. Divide by −7: x = −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=-14

Reference answer

x = -2.

10 − 6 + 3 = 7, so 7x = −14.
Divide both sides by 7: x = −2.
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=0

Reference answer

x = 9.

12 − 8 − 3 = 1, so the variable terms combine to 1x = x.
x − 9 = 0. Add 9 to both sides: x = 9.
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

Reference answer

x = 6.

−2 − 4 + 3 = −3, so −3x + 17 = −1.
Subtract 17: −3x = −18. Divide by −3: x = 6.
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.