Question
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
Answers
GPT-4o mini
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.**
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.**