Grade 7 Expressions: Unit Review

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   Simplify: 2 − 9(x + 5) = −9x + ?

   1. Distribute −9 (the minus sign goes with the 9): multiply each term inside the parentheses by −9. (−9) × x = −9x and (−9) × 5 = −45. So −9(x + 5) becomes −9x − 45.
   2. Now you have 2 − 9x − 45.
   3. Like terms have the same variable part. Here the x-term is −9x; the number terms are 2 and −45.
   4. Combine the number terms: 2 − 45 = −43.
   5. So 2 − 9(x + 5) = −9x − 43.
   6. Match −9x − 43 to −9x + ?: the missing number is −43.

   Answer: −43

2. Example 2

   Simplify: 4(4m − 5) − 8m = ?m − 20

   1. Distribute 4: multiply each term inside the parentheses by 4. 4 × 4m = 16m and 4 × (−5) = −20. So 4(4m − 5) becomes 16m − 20.
   2. Now you have 16m − 20 − 8m.
   3. Like terms have the same variable part. Here the m-terms are 16m and −8m; the number term is −20.
   4. Combine the m-terms by adding their coefficients: 16 − 8 = 8, so they make 8m.
   5. So 4(4m − 5) − 8m = 8m − 20.
   6. Match 8m − 20 to ?m − 20: the missing number is 8.

   Answer: 8

3. Example 3

   Simplify: −9(3n − 7) = ?n + 63

   1. Distribute −9 (the minus sign goes with the 9): multiply each term inside the parentheses by −9. (−9) × 3n = −27n and (−9) × (−7) = 63. So −9(3n − 7) becomes −27n + 63.
   2. Match −27n + 63 to ?n + 63: the missing number is −27.

   Answer: −27