Question

1. solve for y in the equation $8y - 6(-5y - 3) = 18 + 7y$.

no solution
$y = -3$
$y = 7$
$y = 0$

Explanation:

Step1: Distribute the -6

First, we distribute the -6 into the parentheses: \(8y - 6(-5y - 3)=8y + 30y + 18\)

Step2: Combine like terms on left

Combine the \(y\)-terms on the left side: \(8y + 30y + 18 = 38y + 18\)

Step3: Set equal to right side

Now our equation is \(38y + 18 = 18 + 7y\)

Step4: Subtract 7y from both sides

Subtract \(7y\) from both sides: \(38y - 7y + 18 = 18\) which simplifies to \(31y + 18 = 18\)

Step5: Subtract 18 from both sides

Subtract 18 from both sides: \(31y = 18 - 18\) so \(31y = 0\)

Step6: Solve for y

Divide both sides by 31: \(y=\frac{0}{31}=0\)

Answer:

\(y = 0\) (the option "y = 0")