Question

solve for y.
4(y + 4) + 3y = -12
simplify your answer as much as possible.

y =

Explanation:

Step1: Expand the left side

First, we use the distributive property to expand \(4(y + 4)\). The distributive property states that \(a(b + c)=ab+ac\), so \(4(y + 4)=4y+16\). Then the equation becomes:
\(4y + 16+3y=-12\)

Step2: Combine like terms

Next, we combine the like terms \(4y\) and \(3y\) on the left side. Combining like terms means adding their coefficients, so \(4y+3y = 7y\). Now the equation is:
\(7y+16=-12\)

Step3: Isolate the variable term

We want to isolate the term with \(y\), so we subtract 16 from both sides of the equation. Subtracting 16 from both sides gives:
\(7y+16 - 16=-12 - 16\)
Simplifying both sides, we get:
\(7y=-28\)

Step4: Solve for y

Finally, we solve for \(y\) by dividing both sides of the equation by 7. Dividing both sides by 7:
\(\frac{7y}{7}=\frac{-28}{7}\)
Simplifying, we find that:
\(y = - 4\)

Answer:

\(y=-4\)