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 solved the problem correctly Suzie solved the problem correctly 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 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 4 - she divided incorrectly

Answer 1

Let's analyze Suzie's steps to determine if she solved the equation \(9x - 5 = 14(16x + 60)\) correctly.

Starting with the original equation: \[ 9x - 5 = 14(16x + 60) \]

1. Distribute \(14\) on the right side: \[ 9x - 5 = 14 \cdot 16x + 14 \cdot 60 \] \[ 9x - 5 = 224x + 840 \]

So, Step 1 contains a mistake. Suzie incorrectly distributed \( \frac{1}{4} \) instead of \(14\). The correct equation after distributing is: \[ 9x - 5 = 224x + 840 \]

2. The next steps would involve moving terms: Subtract \(224x\) from both sides: \[ 9x - 224x - 5 = 840 \] This simplifies to: \[ -215x - 5 = 840 \]

3. Adding \(5\) to both sides: \[ -215x = 845 \]

4. Dividing by \(-215\): \[ x = -\frac{845}{215} \]

We can simplify that fraction, but it will not yield \(x = 13\).

Therefore, Suzie made a mistake in Step 1 where she incorrectly distributed the \(14\). The correct distribution should have been \(14 \cdot 16x + 14 \cdot 60\).

The correct response is: Suzie made a mistake on Step 1 - she should have distributed the \(14\) to \(16x\) and \(60\) as well.