Suzie solved the equation 9x−5=1/4(16x+60)

Question

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 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.