Sure, let's solve the given equation step by step:
Given equation:
[tex]\[ 3(2y + 4) = 4\left(2y - \frac{1}{2}\right) \][/tex]
1. Distribute the constants on both sides:
On the left side:
[tex]\[ 3 \cdot (2y) + 3 \cdot 4 = 6y + 12 \][/tex]
On the right side:
[tex]\[ 4 \cdot (2y) + 4 \cdot \left(-\frac{1}{2}\right) = 8y - 2 \][/tex]
Therefore, we have:
[tex]\[ 6y + 12 = 8y - 2 \][/tex]
2. Combine like terms:
First, isolate the terms with [tex]\( y \)[/tex] on one side and the constant terms on the other side. To do that, we can subtract [tex]\( 6y \)[/tex] from both sides:
[tex]\[ 6y + 12 - 6y = 8y - 2 - 6y \][/tex]
[tex]\[ 12 = 2y - 2 \][/tex]
3. Isolate the variable [tex]\( y \)[/tex]:
Add 2 to both sides to remove the constant term from the right side:
[tex]\[ 12 + 2 = 2y - 2 + 2 \][/tex]
[tex]\[ 14 = 2y \][/tex]
4. Solve for [tex]\( y \)[/tex]:
Divide both sides by 2:
[tex]\[ \frac{14}{2} = \frac{2y}{2} \][/tex]
[tex]\[ y = 7 \][/tex]
Therefore, the solution is [tex]\( y = 7 \)[/tex].
