Question

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

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.**