Suzie solved the equation 9x - 5 =1/4 (16x + 60 ) using the following steps:

Question

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.
A. Suzie solved for the problem correctly
B. Suzie made a mistake on Step 1 - she should have distributed 1/4 to 60 as well
C. Suzie made a mistake on Step 4 - she divided incorrectly
D. Suzie made a made a mistake on Step 2 - she should have used the addition property instead

Answer 1

To determine if Suzie solved the equation correctly, let's go through each step of her solution and check for errors.

The original equation is: \[ 9x - 5 = \frac{1}{4} (16x + 60) \]

Step 1: Distributing \(\frac{1}{4}\)

Suzie's Step 1: \[ 9x - 5 = 4x + 60 \]

She should have distributed \(\frac{1}{4}\) to both \(16x\) and \(60\): \[ \frac{1}{4}(16x) + \frac{1}{4}(60) = 4x + 15 \] So the correct expression after distribution is: \[ 9x - 5 = 4x + 15 \] This means Suzie made a mistake in Step 1 because she did not distribute to \(60\) properly.

Step 2: Moving \(4x\) to the left side

Suzie's Step 2: \[ 5x - 5 = 60 \]

This is based on her incorrect equation from Step 1. The correct operation should be: \[ 9x - 5 - 4x = 15 \implies 5x - 5 = 15 \]

Step 3: Moving \(-5\)

Suzie's Step 3: \[ 5x = 65 \]

Since she started from an incorrect equation, this step is also incorrect due to the initial error.

Step 4: Dividing by 5

Suzie's Step 4: \[ x = 13 \]

Again, because her earlier steps were incorrect, this is also incorrect.

From this evaluation, we find that Suzie made a mistake in Step 1, and thus the answer is:

B. Suzie made a mistake on Step 1 - she should have distributed 1/4 to 60 as well.