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Suzie solved the equation 9x−5=1/4(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

1 answer

Let's go through Suzie's steps to determine if she solved the equation correctly.

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

  1. Distribute \(\frac{1}{4}\): \[ 9x - 5 = \frac{1}{4}(16x) + \frac{1}{4}(60) \] Calculating those: \[ 9x - 5 = 4x + 15 \] (Suzie's Step 1 was incorrect; she should have gotten \(9x - 5 = 4x + 15\), not \(9x - 5 = 4x + 60\))

  2. Rearranging to isolate variable: From \(9x - 5 = 4x + 15\), we can subtract \(4x\) from both sides: \[ 9x - 4x - 5 = 15 \] This simplifies to: \[ 5x - 5 = 15 \]

  3. Adding 5 to both sides: \[ 5x = 20 \]

  4. Dividing by 5: \[ x = 4 \]

Since Suzie made a mistake in Step 1, she did not distribute the \(\frac{1}{4}\) correctly to the constant \(60\); therefore, all subsequent steps are based on this mistake.

The correct answer is: Suzie made a mistake on Step 1 - she should have distributed the 1/4 to 60 as well.