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Combining like terms

Collect the x terms and constants to simplify an expression.

Practice + answer key · 2 pages

Worksheet settings12 questions · 2 columns · A4
Coefficients and constants

Choose the numbers in front of x and the numbers without x. Negative values are allowed.

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Combining like termsCombining like terms. Practice. Combine like terms: x − 7 + 0 − 5. Combine like terms: 8x + 7 + 5x − 9. Combine like terms: 6x − 3 − 5x − 7. Combine like terms: −7x − 4 − 2x − 4. Combine like terms: −4x − 5 + 3x + 3. Combine like terms: 3x + 1 + 0 − 3. Combine like terms: 4x − 1 − x − 3. Combine like terms: −3x − 5 + 6x + 1. Combine like terms: −8x − 1 + 0 + 0. Combine like terms: 3x − 1 + 8x − 1. Combine like terms: −8x + 7 + 7x + 5. Combine like terms: x + 7 − 9x + 0.Name __________________________Date _______________Combining like termsCombine like terms.Worked exampleSimplify 3x + 5 − 2x + 7. → x + 12(3 − 2)x + (5 + 7)1.Combine like terms: x − 7 + 0 −5.2.Combine like terms: 8x + 7 + 5x −9.3.Combine like terms: 6x − 3 − 5x −7.4.Combine like terms: −7x − 4 − 2x− 4.5.Combine like terms: −4x − 5 + 3x+ 3.6.Combine like terms: 3x + 1 + 0 −3.7.Combine like terms: 4x − 1 − x −3.8.Combine like terms: −3x − 5 + 6x+ 1.9.Combine like terms: −8x − 1 + 0 +0.10.Combine like terms: 3x − 1 + 8x −1.11.Combine like terms: −8x + 7 + 7x+ 5.12.Combine like terms: x + 7 − 9x +0.MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 1mathsprig-1 · mathsprig-v1 · 496cd7f0
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Practice + answer key · 2 pages

Algebra

What you’ll practice

Simplify an expression with two x terms and two constants.

Keep terms with x together and numbers without x together. Add each group separately, taking the sign with every term.

How this skill works

Write the two x terms together and the constants together, keeping their signs.

Add the x coefficients. Add the constants. An x term with coefficient zero disappears.

Worked example

Simplify 3x + 5 − 2x + 7.
  1. (3 − 2)x + (5 + 7)
  2. 1x + 12
  3. x + 12

Answer: x + 12

Teaching notes

  • 3x + 5 cannot become 8x because 5 has no x.
Practice questions
  1. Combine like terms: x − 7 + 0 − 5.
  2. Combine like terms: 8x + 7 + 5x − 9.
  3. Combine like terms: 6x − 3 − 5x − 7.
  4. Combine like terms: −7x − 4 − 2x − 4.
  5. Combine like terms: −4x − 5 + 3x + 3.
  6. Combine like terms: 3x + 1 + 0 − 3.
  7. Combine like terms: 4x − 1 − x − 3.
  8. Combine like terms: −3x − 5 + 6x + 1.
  9. Combine like terms: −8x − 1 + 0 + 0.
  10. Combine like terms: 3x − 1 + 8x − 1.
  11. Combine like terms: −8x + 7 + 7x + 5.
  12. Combine like terms: x + 7 − 9x + 0.
Answers and steps
  1. x − 12
    1. Combine the x coefficients: 1 + (0) = 1.
    2. Combine constants: −7 + (−5) = −12.
    3. The simplified expression is x − 12.
  2. 13x − 2
    1. Combine the x coefficients: 8 + (5) = 13.
    2. Combine constants: 7 + (−9) = −2.
    3. The simplified expression is 13x − 2.
  3. x − 10
    1. Combine the x coefficients: 6 + (−5) = 1.
    2. Combine constants: −3 + (−7) = −10.
    3. The simplified expression is x − 10.
  4. −9x − 8
    1. Combine the x coefficients: −7 + (−2) = −9.
    2. Combine constants: −4 + (−4) = −8.
    3. The simplified expression is −9x − 8.
  5. −x − 2
    1. Combine the x coefficients: −4 + (3) = −1.
    2. Combine constants: −5 + (3) = −2.
    3. The simplified expression is −x − 2.
  6. 3x − 2
    1. Combine the x coefficients: 3 + (0) = 3.
    2. Combine constants: 1 + (−3) = −2.
    3. The simplified expression is 3x − 2.
  7. 3x − 4
    1. Combine the x coefficients: 4 + (−1) = 3.
    2. Combine constants: −1 + (−3) = −4.
    3. The simplified expression is 3x − 4.
  8. 3x − 4
    1. Combine the x coefficients: −3 + (6) = 3.
    2. Combine constants: −5 + (1) = −4.
    3. The simplified expression is 3x − 4.
  9. −8x − 1
    1. Combine the x coefficients: −8 + (0) = −8.
    2. Combine constants: −1 + (0) = −1.
    3. The simplified expression is −8x − 1.
  10. 11x − 2
    1. Combine the x coefficients: 3 + (8) = 11.
    2. Combine constants: −1 + (−1) = −2.
    3. The simplified expression is 11x − 2.
  11. −x + 12
    1. Combine the x coefficients: −8 + (7) = −1.
    2. Combine constants: 7 + (5) = 12.
    3. The simplified expression is −x + 12.
  12. −8x + 7
    1. Combine the x coefficients: 1 + (−9) = −8.
    2. Combine constants: 7 + (0) = 7.
    3. The simplified expression is −8x + 7.