Question

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.

Answer 1

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

1. The given equation is:
\[
9x - 5 = \frac{1}{4}(16x + 60)
\]
Distributing \(\frac{1}{4}\) on the right side:
\[
\frac{1}{4}(16x) + \frac{1}{4}(60) = 4x + 15
\]

So the equation should be:
\[
9x - 5 = 4x + 15
\]
**This means Suzie made a mistake in Step 1.**

2. Let's follow the corrected form of the equation:
\[
9x - 5 = 4x + 15
\]
Next, we apply the subtraction property of equality to move \(4x\) to the left side:
\[
9x - 4x - 5 = 15
\]
This simplifies to:
\[
5x - 5 = 15
\]
(This part was done correctly in her Step 2.)

3. Now, we will use the addition property of equality to move \(-5\):
\[
5x = 15 + 5
\]
Which simplifies to:
\[
5x = 20
\]
(This also implies she made a mistake in her Step 3.)

4. Finally, we use the division property of equality:
\[
x = \frac{20}{5} = 4
\]
So the final solution is:
\[
x = 4
\]

Thus, Suzie's final answer that \(x = 13\) is incorrect. The mistakes occurred in Step 1 (incorrect distribution) and subsequently in Step 3 (incorrect value carried over). The correct solution to the equation \(9x - 5 = \frac{1}{4}(16x + 60)\) is \(x = 4\).