Question

solve the equation below. whats the value of $v$?
there are only $v$ terms on the right side. what move can you make next to get no $v$ on the left, while keeping the equation balanced?
$\frac{1}{2}(12v - 8)=8v + 10$
$6v - 4=8v + 10$
options:
multiply both sides by $6v$
divide both sides by $6v$
add $6v$ to both sides
subtract $6v$ from both sides

Explanation:

Step1: Simplify left-hand side

$\frac{1}{2}(12v - 8) = 6v - 4$

Step2: Align simplified equation

$6v - 4 = 8v + 10$

Step3: Isolate variable terms

Subtract $6v$ from both sides:
$6v - 4 - 6v = 8v + 10 - 6v$
$-4 = 2v + 10$

Step4: Isolate the $v$-term

Subtract 10 from both sides:
$-4 - 10 = 2v + 10 - 10$
$-14 = 2v$

Step5: Solve for $v$

Divide both sides by 2:
$\frac{-14}{2} = \frac{2v}{2}$
$v = -7$

Answer:

To get no $v$-terms on the right, subtract $6v$ from both sides.
The value of $v$ is $\boldsymbol{-7}$