Let's examine each step that Riley took while solving the equation.
Step 1:
[tex]\[ -2x + 4 = 3 \][/tex]
This is the starting equation.
Step 2:
[tex]\[ -2x + 4 - 4 = 3 - 4 \][/tex]
In this step, Riley is subtracting 4 from both sides of the equation to isolate the term with [tex]\( x \)[/tex]. Let’s simplify both sides:
[tex]\[ -2x + 4 - 4 = -2x \][/tex]
[tex]\[ 3 - 4 = -1 \][/tex]
So, the equation is simplified to:
[tex]\[ -2x = -1 \][/tex]
Step 3:
[tex]\[ -2x = -1 \][/tex]
This shows the result from Step 2.
Step 4:
[tex]\[ \frac{-2x}{2} = \frac{-1}{2} \][/tex]
Here, Riley is dividing both sides of the equation by -2 to solve for [tex]\( x \)[/tex]. Simplifying the left side:
[tex]\[ \frac{-2x}{2} = x \][/tex]
And the right side:
[tex]\[ \frac{-1}{2} = -\frac{1}{2} \][/tex]
So, we get:
[tex]\[ x = -\frac{1}{2} \][/tex]
Step 5:
[tex]\[ x = -\frac{1}{2} \][/tex]
This is the result from Step 4.
Now, let’s verify the steps:
The simplification in Step 2 results in:
[tex]\[ -2x = -1 \][/tex]
which is correct.
Dividing both sides by -2 in Step 4 results in:
[tex]\[ x = -\frac{1}{2} \][/tex]
which is also correct.
Thus, the final solution matches the steps preceding it correctly.
Therefore, the true statement is:
Riley solved the equation correctly.
