Select the correct answer.

Question

Irene made a mistake when she solved this inequality:

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

Between which two consecutive steps did Irene make a mistake?

A.
step 1 and step 2
B.
step 2 and step 3
C.
step 3 and step 4
D.
step 4 and step 5

Answer 1

To find the mistake made by Irene, let's analyze each step of her solution:

1. Step 1: \(-6(x + 3) + 10 < -2\) (This step is correct)

2. Step 2: Distributing \(-6\) gives us \(-6x - 18 + 10 < -2\). (This step is also correct, as \(-6(x + 3) = -6x - 18\))

3. Step 3: Combining \(-18\) and \(10\) gives us \(-6x - 8 < -2\) (This step is correct.)

4. Step 4: To isolate \(-6x\), she adds \(8\) to both sides: \(-6x - 8 + 8 < -2 + 8\) becomes \(-6x < 6\) (This step is also correct.)

5. Step 5: To solve for \(x\), she divides both sides by \(-6\), remembering to reverse the inequality: \(-6x < 6\) becomes \(x > -1\). (This step is incorrect because Irene incorrectly stated the final result; it should be \(x > -1\) instead of \(x < -1\).)

Thus, the mistake occurs between step 4 and step 5.

The correct answer is:

D. step 4 and step 5