Let's carefully analyze each step of the solution provided by Riley, ensuring that no mistakes are made:
1. Step 1: [tex]\( -2x + 4 = 3 \)[/tex]
This is the original equation.
2. Step 2: [tex]\( -2x + 4 - 4 = 3 - 4 \)[/tex]
[tex]\( -2x = -1 \)[/tex]
Riley correctly subtracted 4 from both sides to isolate the term involving [tex]\( x \)[/tex]. So far, this step is correct.
3. Step 3: [tex]\( -2x = -1 \)[/tex]
This is a simplified version of the previous step, and it is correctly copied.
4. Step 4: [tex]\( \frac{-2x}{2} = \frac{-1}{2} \)[/tex]
Here Riley made a mistake. When dividing by the coefficient of [tex]\( x \)[/tex], which is -2, the correct division should be:
[tex]\[
\frac{-2x}{-2} = \frac{-1}{-2}
\][/tex]
Simplifying, we get:
[tex]\[
x = \frac{-1}{-2} = \frac{1}{2}
\][/tex]
Riley incorrectly divided by 2 instead of -2, leading to an incorrect value for [tex]\( x \)[/tex].
5. Step 5: [tex]\( x = -\frac{1}{2} \)[/tex]
Based on the incorrect division in Step 4, Riley arrived at the wrong solution.
Therefore, Riley made a mistake in Step 4. The corrected value for [tex]\( x \)[/tex] should be [tex]\( \frac{1}{2} \)[/tex].
So, the correct statement is:
- Riley made a mistake in step 4.
