To solve the equation [tex]\( 2(3y - 4) = 3\left(y - \frac{2}{3}\right) \)[/tex], follow these steps:
1. Distribute the numbers outside the parentheses:
- For the left side: [tex]\( 2 \cdot (3y - 4) \)[/tex]:
[tex]\[
2 \cdot 3y - 2 \cdot 4 = 6y - 8
\][/tex]
- For the right side: [tex]\( 3 \cdot \left( y - \frac{2}{3} \right) \)[/tex]:
[tex]\[
3 \cdot y - 3 \cdot \frac{2}{3} = 3y - 2
\][/tex]
2. Rewrite the equation with the distributed terms:
[tex]\[
6y - 8 = 3y - 2
\][/tex]
3. Isolate the [tex]\( y \)[/tex]-terms on one side of the equation:
- Subtract [tex]\( 3y \)[/tex] from both sides:
[tex]\[
6y - 3y - 8 = 3y - 3y - 2
\][/tex]
Simplify:
[tex]\[
3y - 8 = -2
\][/tex]
4. Move the constant term to the other side to isolate the [tex]\( y \)[/tex]-term:
- Add 8 to both sides:
[tex]\[
3y - 8 + 8 = -2 + 8
\][/tex]
Simplify:
[tex]\[
3y = 6
\][/tex]
5. Solve for [tex]\( y \)[/tex] by dividing both sides by the coefficient of [tex]\( y \)[/tex]:
[tex]\[
y = \frac{6}{3}
\][/tex]
Simplify:
[tex]\[
y = 2
\][/tex]
Therefore, the solution is [tex]\( y = 2 \)[/tex].
The solution is [tex]\( \boxed{2} \)[/tex].
