Question

A student solves the following problem: 2(x - 2) + 5x = 24

Step 1: 2x - 4 + 5x = 24

Step 2: 10x - 4 = 24

Step 3: 10x - 4 + 4 = 24 + 4

Step 4: 10x = 28

Step 5: 10x/10=28/10

Step 6: x = 2.8



Where is the mistake? What did the student do incorrectly?

Answer 1

The student made a mistake in Step 2. Let's break down the solution to find the error:

1. **Original equation**: \(2(x - 2) + 5x = 24\)
2. **Step 1 (Correct)**: Distributing the 2 gives \(2x - 4 + 5x = 24\).
3. **Step 2 (Incorrect)**: The student writes \(10x - 4 = 24\), which is wrong. The correct combination of like terms from Step 1 is:
\[
2x + 5x - 4 = 24 \implies 7x - 4 = 24.
\]

So instead of \(10x - 4 = 24\), it should have been \(7x - 4 = 24\).

Continuing from this correct step:
4. **Step 3 (incorrect based on previous error)**: The equation would instead be:
\[
7x - 4 + 4 = 24 + 4 \implies 7x = 28.
\]
5. **Step 4 (now requires correction)**: Now divide both sides by 7:
\[
x = \frac{28}{7} = 4.
\]

Thus, **the correct solution is \(x = 4\)**, not \(x = 2.8\). The error occurred in Step 2 where the student incorrectly combined the coefficients of \(x\).