Suzie solved the equation 9x−5=14(16x+60) using the following steps: 1) Distribute 1/4 to get 9x−5=4x+60 2) Use subtraction property of equality to move 4x to get 5x−5=60 3) Use addition property of equality to move 5 and get 5x=65 4) Use division property of equality to get x=13 Determine if Suzie solved correctly - if not, identify which step was the mistake. (1 point) Responses Suzie made a mistake on Step 2 - she should have used the addition property instead Suzie made a mistake on Step 2 - she should have used the addition property instead Suzie made a mistake on Step 1 - she should have distributed the 1/4 to 60 as well Suzie made a mistake on Step 1 - she should have distributed the 1/4 to 60 as well Suzie solved the problem correctly Suzie solved the problem correctly Suzie made a mistake on Step 4 - she divided incorrectly

Answer 1

To determine whether Suzie solved the equation \(9x - 5 = 14(16x + 60)\) correctly, let's go through her steps one by one.

1. Step 1: Distribute
   Suzie claims to distribute \( \frac{1}{4} \). However, the left side is actually \( 9x - 5 \) and the right side is \( 14(16x + 60) \), which should have been distributed instead of applying \( \frac{1}{4} \). The correct distribution would be: \[ 14(16x) + 14(60) = 224x + 840 \] So the equation after distributing should be: \[ 9x - 5 = 224x + 840 \]

2. Step 2: Move terms
   Suzie's Step 2 subtracts \(4x\) incorrectly from the distribution. Based on the original equation after distributing, she should instead move \(224x\) from the right side to the left side, resulting in: \[ 9x - 224x - 5 = 840 \] Which simplifies to: \[ -215x - 5 = 840 \]

3. Step 3: Add 5
   After this, Suzie should correctly apply the addition property to move \(-5\) to the right side: \[ -215x = 840 + 5 = 845 \]

4. Step 4: Divide
   Finally, she would divide by \(-215\) to solve for \(x\).

From the analysis, it is clear that Suzie made a mistake in Step 1 by incorrectly using \( \frac{1}{4} \).

Therefore, the correct response is: Suzie made a mistake on Step 1 - she should have distributed the \(14\) to both \(16x\) and \(60\) instead.