Question

3. A student solved the following equation using the following steps:

4(2−3x)=x−2(2x+1)

8−3x=x−4x−2

8−3x=−3x−2

Answer 1

Let's review the steps the student took to solve the equation \( 4(2 - 3x) = x - 2(2x + 1) \) step-by-step to verify the correctness.

1. **Distribute** on the left-hand side:
\[
4 \cdot 2 - 4 \cdot 3x = 8 - 12x
\]
Therefore, the left side becomes:
\[
8 - 12x
\]

2. **Distribute** on the right-hand side:
\[
-2(2x + 1) = -4x - 2
\]
Therefore, the right side becomes:
\[
x - 4x - 2 = -3x - 2
\]

Putting that together, we now have:
\[
8 - 12x = -3x - 2
\]

The student then wrote:
\[
8 - 3x = -3x - 2
\]
This isn’t correct in terms of what was stated. Instead, you should have:
\[
8 - 12x = -3x - 2
\]

Now, let's proceed to solve the equation correctly from:
\[
8 - 12x = -3x - 2
\]

3. **Add \(12x\) to both sides**:
\[
8 = 12x - 3x - 2
\]
\[
8 = 9x - 2
\]

4. **Add \(2\) to both sides**:
\[
8 + 2 = 9x
\]
\[
10 = 9x
\]

5. **Divide by \(9\)**:
\[
x = \frac{10}{9}
\]

Thus, the solution to the equation is:
\[
x = \frac{10}{9}
\]

The original steps included an incorrect transformation. Be careful during distribution and combining like terms.