Answer: To write equivalent expressions for the length of a rectangle, we can use the distributive property and the commutative property of addition. The distributive property allows us to multiply a factor by a sum or difference by multiplying each term inside the parentheses by the factor. The commutative property of addition allows us to change the order of the terms in an expression without changing its value.
Step-by-step explanation: Here are three different equivalent expressions for the length of the rectangle:
- 5(3x+2) + 14x+17 = 15x + 10 + 14x + 17 = (15x + 14x) + (10 + 17) = 29x + 27
- 5(3x+2) + 14x+17 = (5*3x) + (5*2) + 14x + 17 = 15x + 10 + 14x + 17 = (10 + 17) + (15x + 14x) = 27 + 29x
- 5(3x+2) + 14x+17 = (5*3x) + (5*2) + (14x + 17) = (15x + 14x) + (5*2 + 17) = (15x + 14x) + (10 + 17) = (15x + 14x) + 27 = 29x + 27
