Example Mia babysits some children after school. For each child, she
charges x + 2 dollars per hour. One day she cared for 2
children for 3 hours each. She paid 54 per child for materials
for activities. Two students wrote expressions for the amount
of money Mia earned. Are their expressions equivalent?
Paolo wrote the expression 3(x + 2) + 3(x + 2) - 8.
Carla wrote the expression (3x + 6) - 4+ (3x + 6) - 4.
Simplify the expressions to see whether they are equivalent.
Paolo's Expression Carla's Expression
3(x + 2) + 3x + 2) - 8 (3x + 6) - 4+ (3x + 6) - 4
- 3x + 6 + 3x + 6-8 3x + 3x + 6 + 6 - 4 - 4
6x + 4
= 6x + 4
The expressions are equivalent.
Why did Paolo add 3(x + 2) to itself and subtract 8?