Solve the equation.

Question

4 left parenthesis 3 y minus 1 right parenthesis minus 3 left parenthesis 2 y right parenthesis equals 12
Question content area bottom
Part 1
yequals
  
enter your response here
​(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:

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