Question

Step 1: 4x + 5 < 6x + 1 (Given)
Step 2: −2x + 5 < 1 (Subtraction)
Step 3: −2x < 6 (Addition)
Step 4: x > −3 (Division)

Mia is trying to find her mistake in the problem shown. In which step did she first make a mistake

A Step 1
B Step 2
C Step 3
D Step 4

Answer 1

Let's analyze each step to identify any mistakes:

1. **Step 1:** \( 4x + 5 < 6x + 1 \) - This step is correct as it is the original inequality.

2. **Step 2:** \( -2x + 5 < 1 \) - To get this, Mia subtracted \(6x\) from both sides and also subtracted \(5\) from both sides. The correct subtraction should be:
- Subtract \(4x\) from both sides:
\[
5 < 2x + 1
\]
- Then subtract \(1\) from both sides:
\[
4 < 2x
\]
This implies \( -2x + 5 < 1 \) is not correct.

3. **Step 3:** \( -2x < 6 \) - This step is based on Step 2's result but also doesn't follow accurately from the previous step.

4. **Step 4:** \( x > -3 \) - To obtain this, Mia would divide the inequality (assuming step 3 was somehow correct) by \(-2\), which would flip the inequality. Since the previous steps were incorrect, the conclusion here (i.e., \( x > -3 \)) does not follow.

The mistake first occurs at **Step 2**, where she incorrectly manipulated the original inequality.

Therefore, the correct answer is **B Step 2.**