Question

Ashley solves the equation 0.4(2.5 x - 8) - 4 and claims that the solution is x - -0.8. The table below shows the steps she took and the reasons for each step.

Step
1
2
Equation
0.4(2.5 x-8)= -4
X-32=-4
x - 32+3.2 = -4 +32
x=-08
Reason
Given
Associative Property
Addition Property of Equality
Subtraction Property of Equality
Determine whether each statement below is true or false regarding the reasons given in the table. Select True or False for each statement.
True False
The reason for Step 1 is correct
The reason for Step 1 should be the Distributive Property
The reason for Step 2 is correct
The reason for Step 2 should be the Additive Identity Property
The reason for Step 3 is correct
The reason for Step 3 should be Additive Inverses Property and/or Combining Like Terms

Answer 1

The reason for Step 1 is correct . False

The reason for Step 1 should be the Distributive Property . True

The reason for Step 2 is correct . True

The reason for Step 2 should be the Additive Identity Property . False

The reason for Step 3 is correct . False

The reason for Step 3 should be Additive Inverses Property and/or Combining Like Terms. True

Explanation:

Distributive Property: a(b + c) = ab + ac

Addition property of equality: if x = y then x + a = y + a

Subtraction property of equality: if x = y then x - a = y - a