Step 1: 4x + 5 < 6x + 1 (Given)

Question

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.