Question

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 $-6x < 6$.

• Option A (transitive property) relates to if $a < b$ and $b < c$, then $a < c$, which is not applicable here.
• Option B (division property) involves dividing both sides, but here we added, not divided.
• Option C (distribution property) is about expanding expressions (like $a(b + c) = ab + ac$), which is not used here.
• Option D (addition property of inequality) matches the operation of adding 8 to both sides.

Answer:

D. addition property of inequality