Question

8(y+4)-2(y-1)=70-3y
Solve the equation. You must show ALL work to earn full credit.

Answer 1

We start with the equation:

\[
8(y + 4) - 2(y - 1) = 70 - 3y
\]

**Step 1: Distribute terms on the left side.**

Distributing \(8\) to \((y + 4)\):

\[
8y + 32
\]

Distributing \(-2\) to \((y - 1)\):

\[
-2y + 2
\]

Now substitute these back into the equation:

\[
8y + 32 - 2y + 2 = 70 - 3y
\]

Combine like terms on the left side:

\[
(8y - 2y) + (32 + 2) = 70 - 3y
\]
\[
6y + 34 = 70 - 3y
\]

**Step 2: Move all \(y\) terms to one side and constant terms to the other side.**

Add \(3y\) to both sides:

\[
6y + 3y + 34 = 70
\]
\[
9y + 34 = 70
\]

Next, subtract \(34\) from both sides:

\[
9y + 34 - 34 = 70 - 34
\]
\[
9y = 36
\]

**Step 3: Solve for \(y\).**

Divide both sides by \(9\):

\[
y = \frac{36}{9}
\]
\[
y = 4
\]

**Final Answer:**

The solution to the equation is

\[
\boxed{4}
\]