Question

read the problem below. The problem was solved incorrectly. Explain the mistake made down below and why its incorrect.

3x + 2x - 6=24
-2x -2x
x-6=24
+6 +6

x=30

Answer 1

Let's look at the steps in the problem-solving process for the equation \(3x + 2x - 6 = 24\) and identify where the mistake occurred.

1. Start with the original equation:
\[ 3x + 2x - 6 = 24 \]

2. Combine like terms on the left side. The terms \(3x\) and \(2x\) can be added together:
\[ 5x - 6 = 24 \]

3. The next step should involve isolating \(x\). The incorrect solution showed:
\[ -2x - 2x \]
**This step is incorrect.** Instead of subtracting \(2x\) from both sides, you should add \(6\) to both sides to isolate the term with \(x\):
\[ 5x - 6 + 6 = 24 + 6 \]

This simplifies to:
\[ 5x = 30 \]

4. Then, divide both sides by \(5\) to solve for \(x\):
\[ x = \frac{30}{5} = 6 \]

So, the mistake in the original solution was incorrectly subtracting \(2x\) instead of correctly adding \(6\) to isolate the \(5x\) term. This led to the wrong conclusion that \(x = 30\). The correct answer is \(x = 6\).