Question

Solve the equation.
4 left parenthesis 3 y minus 1 right parenthesis minus 3 left parenthesis 2 y right parenthesis equals 12
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Part 1
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​(Type an integer or a simplified​ fraction.)

Answer 1

To solve the equation

\[ 4(3y - 1) - 3(2y) = 12, \]

we first distribute the terms:

1. Distributing \( 4 \) in \( 4(3y - 1) \):
\[
4 \cdot 3y - 4 \cdot 1 = 12y - 4.
\]

2. Distributing \( -3 \) in \( -3(2y) \):
\[
-3 \cdot 2y = -6y.
\]

Now, substituting back into the equation, we have:

\[
12y - 4 - 6y = 12.
\]

Next, we combine like terms:

\[
(12y - 6y) - 4 = 12 \implies 6y - 4 = 12.
\]

Now, we isolate \( y \) by adding \( 4 \) to both sides:

\[
6y - 4 + 4 = 12 + 4 \implies 6y = 16.
\]

Finally, divide both sides by \( 6 \):

\[
y = \frac{16}{6} = \frac{8}{3}.
\]

Thus, the solution is:

\[
y = \frac{8}{3}.
\]