Question

Suzie solved the equation 9x-5=1/4(16x+60) using the following steps. Step 1: 36x-20=16x+60 Step 2: 20x-20=60 Step 3: 20x=80 Step 4: x=4 Determine the step in which she made a mistake, if any.

Answer 1

Let's go through Suzie's steps to identify if and where she made a mistake while solving the equation \( 9x - 5 = \frac{1}{4}(16x + 60) \).

Starting with the original equation:

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

**Step 1: Distributing \(\frac{1}{4}\) on the right side:**
\[
\frac{1}{4}(16x + 60) = \frac{1}{4} \cdot 16x + \frac{1}{4} \cdot 60 = 4x + 15
\]

This means the equation is:
\[
9x - 5 = 4x + 15
\]

**Step 2: Subtract \(4x\) from both sides:**
\[
9x - 4x - 5 = 15
\]
This simplifies to:
\[
5x - 5 = 15
\]

**Step 3: Add 5 to both sides:**
\[
5x = 15 + 5
\]
This simplifies to:
\[
5x = 20
\]

**Step 4: Divide by 5:**
\[
x = \frac{20}{5} = 4
\]

Now let's compare this to Suzie's steps:

- In **Step 1**, she claims to have \(36x - 20 = 16x + 60\). This is incorrect. The correct equation after moving the terms around should have been \(9x - 4x - 5 = 15\), resulting in \(5x - 5 = 15\).

It's clear she made a mistake in her calculations during the first step after distributing the \(\frac{1}{4}\). Therefore, she made a mistake in **Step 1**.