Question

Solve for x:

2(6 − 2x) + 3x = 4 + 2(5 + x)

Answer 1

To solve the equation \( 2(6 - 2x) + 3x = 4 + 2(5 + x) \), we will start by expanding both sides.

1. Distribute on the left side:
\[
2(6) - 2(2x) + 3x = 12 - 4x + 3x = 12 - x
\]

2. Distribute on the right side:
\[
4 + 2(5) + 2(x) = 4 + 10 + 2x = 14 + 2x
\]

Now, our equation looks like this:
\[
12 - x = 14 + 2x
\]

3. Next, we isolate \( x \) by adding \( x \) to both sides:
\[
12 = 14 + 3x
\]

4. Then, subtract \( 14 \) from both sides:
\[
12 - 14 = 3x \implies -2 = 3x
\]

5. Finally, divide both sides by \( 3 \):
\[
x = -\frac{2}{3}
\]

Thus, the solution is:
\[
\boxed{-\frac{2}{3}}
\]