Question

riley solved an equation, as shown in the table.

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$$\begin{tabular}{|c|c|} \\hline step & statement \\\\ \\hline 1 & \\(-2x + 4 = 3\\) \\\\ \\hline 2 & \\(-2x + 4 - 4 = 3 - 4\\) \\\\ \\hline 3 & \\(-2x = -1\\) \\\\ \\hline 4 & \\(\\frac{2x}{2} = \\frac{-1}{2}\\) \\\\ \\hline 5 & \\(x = -\\frac{1}{2}\\) \\\\ \\hline \\end{tabular}$$

which statement is true?

• riley made a mistake in step 2.
• riley made a mistake in step 4.
• riley made a mistake in step 5.
• riley solved the equation correctly.

Explanation:

Analyze the given steps

We examine each step of Riley's solution to find any algebraic errors:

• Step 1: The starting equation is:

$$ -2x + 4 = 3 $$

• Step 2: Riley subtracts \(4\) from both sides:

$$ -2x + 4 - 4 = 3 - 4 $$

This is a mathematically valid operation.

• Step 3: Simplifying both sides:
• Left side: \(-2x + 4 - 4 = -2x\)
• Right side: \(3 - 4 = -1\)
• Resulting equation: \(-2x = -1\). This is correct.
• Step 4: Riley attempts to isolate \(x\) by dividing both sides. The equation shown is:

$$ \frac{2x}{2} = \frac{-1}{2} $$

However, the left side of the equation in Step 3 was \(-2x\), not \(2x\). To solve correctly, Riley should have divided by \(-2\):

$$ \frac{-2x}{-2} = \frac{-1}{-2} $$

By changing \(-2x\) to \(2x\) on the left side while keeping the right side as \(\frac{-1}{2}\), Riley made a sign error. Thus, Step 4 is incorrect.

Identify the correct statement

Since the error occurs in the transition to Step 4, the statement "Riley made a mistake in step 4" is true.

Answer:

• Riley made a mistake in step 2.
• Riley made a mistake in step 4. (Correct answer)
• Riley made a mistake in step 5.
• Riley solved the equation correctly.