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
\[ \boxed{4} \]
1 answer