Question

Paula used these steps to solve an equation:

Step 1: -4(7 + 8) - 21 = 25
Step 2: -4r – 32 - 2x = 25
Step 3: -61 – 32 = 25
Step 4: -6x = 57
Step 5: x = -95
Between which two steps did Paula use the division property of equality?

Answer 1

Between step 4 and step 5

Explanation:

The Division Property of Equality states that when both sides of an equation are divided by the same nonzero number, both sides remain equal.

That is, if a, b, and c are real numbers such that a = b and c ≠0, then

`(a)/(c) = (b)/(c)`

At step 4: The equation was -6x = 57

To move to step 5, Paula had to divide both sides by the co-efficient of x (-6) in order to get the value of x. See below

`-6x = 57` ---- Divide both sides by -6 (Step 4)

`(-6x)/(-6) = (57)/(-6)` ---- (Intermediary between step 4 and 5)

`x = -9.5` ----- Step 5

Hence, we can conclude that the division property of equality was done between step 4 and step 5