Question

select the correct answer.
michael solved this inequality as shown:
step 1: -6(x + 3) + 10 < -2
step 2: -6x − 18 + 10 < -2
step 3: -6x − 8 < -2
step 4: -6x < 6
step 5: x > -1
what property justifies the work shown between step 3 and step 4?
a. transitive property
b. division property of inequality
c. distribution property
d. addition property of inequality

Explanation:

To determine the property justifying the transition from Step 3 ($-6x - 8 < -2$) to Step 4 ($-6x < 6$), we analyze the operation: adding 8 to both sides of the inequality. The addition property of inequality states that if we add the same number to both sides of an inequality, the inequality remains true. Here, adding 8 to both sides eliminates the -8 on the left, resulting in $-6x < 6$. The transitive property relates to equal/unequal relationships between three quantities, the division property involves dividing both sides, and the distribution (distributive) property is about multiplying over a sum/difference (not applicable here). So the addition property of inequality applies.

Answer:

D. addition property of inequality