Grade 7 Expressions: Equivalent Expressions

Worked examples

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

1. Example 1

   Simplify: 7(6x + 8) − 7x = ?x + 56

   1. Distribute 7: multiply each term inside the parentheses by 7. 7 × 6x = 42x and 7 × 8 = 56. So 7(6x + 8) becomes 42x + 56.
   2. Now you have 42x + 56 − 7x.
   3. Like terms have the same variable part. Here the x-terms are 42x and −7x; the number term is 56.
   4. Combine the x-terms by adding their coefficients: 42 − 7 = 35, so they make 35x.
   5. So 7(6x + 8) − 7x = 35x + 56.
   6. Match 35x + 56 to ?x + 56: the missing number is 35.

   Answer: 35

2. Example 2

   Simplify: a − 0.1a = ?a

   1. Like terms have the same variable part. Here the a-terms are a and −0.1a.
   2. Combine the a-terms by adding their coefficients: 1 − 0.1 = 0.9, so they make 0.9a.
   3. So a − 0.1a = 0.9a.
   4. Match 0.9a to ?a: the missing number is 0.9.

   Answer: 0.9

3. Example 3

   Simplify: 2(y − 4) − 4(y + 4) = −2y + ?

   1. Distribute 2: multiply each term inside the parentheses by 2. 2 × y = 2y and 2 × (−4) = −8. So 2(y − 4) becomes 2y − 8.
   2. Distribute −4 (the minus sign goes with the 4): multiply each term inside the parentheses by −4. (−4) × y = −4y and (−4) × 4 = −16. So −4(y + 4) becomes −4y − 16.
   3. Now you have 2y − 8 − 4y − 16.
   4. Like terms have the same variable part. Here the y-terms are 2y and −4y; the number terms are −8 and −16.
   5. Combine the y-terms by adding their coefficients: 2 − 4 = −2, so they make −2y.
   6. Combine the number terms: −8 − 16 = −24.
   7. So 2(y − 4) − 4(y + 4) = −2y − 24.
   8. Match −2y − 24 to −2y + ?: the missing number is −24.

   Answer: −24