Suzie solved the equation 9x−5=1 over 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.

options:

Suzie made a mistake on Step 4 - she divided incorrectly
Suzie made a mistake on Step 4 - she divided incorrectly

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 solved the problem correctly

Answer 1

Let's review Suzie's solution step by step, starting with the original equation:

\[ 9x - 5 = \frac{1}{4}(16x + 60) \]

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

Suzie's first step is to distribute \( \frac{1}{4} \). The correct distribution should be: \[ \frac{1}{4}(16x + 60) = \frac{1}{4} \cdot 16x + \frac{1}{4} \cdot 60 = 4x + 15 \] Therefore, the equation \[ 9x - 5 = 4x + 15 \] is what she should have obtained, not \( 9x - 5 = 4x + 60 \).

2. Step 2: Subtracting \( 4x \)

Since Step 1 was incorrect, this step follows the incorrect equation. Instead of subtracting \( 4x \) from both sides resulting in: \[ 5x - 5 = 60 \] it should have resulted in: \[ 5x - 5 = 15 \]

3. Step 3: Adding 5

Again, since the equation was wrong, moving to this step is also based on an incorrect premise: \[ 5x = 15 + 5 \Rightarrow 5x = 20 \]

4. Step 4: Dividing by 5

Finally, this step is based on the incorrect equation: \[ x = \frac{20}{5} = 4 \]

Conclusion

Suzie made a mistake in Step 1 - she should have distributed the \( \frac{1}{4} \) correctly to both terms, including the \( 60 \), resulting in \( 15 \) instead of \( 60 \).

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