Question

solve for v.
-3v + 11 = -8v + 51
simplify your answer as much as possible.

Explanation:

Step1: Add \( 8v \) to both sides

To get all the \( v \)-terms on one side, we add \( 8v \) to both sides of the equation \( -3v + 11 = -8v + 51 \). This gives us \( -3v + 8v + 11 = -8v + 8v + 51 \), which simplifies to \( 5v + 11 = 51 \).

Step2: Subtract 11 from both sides

Next, we want to isolate the term with \( v \). So we subtract 11 from both sides: \( 5v + 11 - 11 = 51 - 11 \), which simplifies to \( 5v = 40 \).

Step3: Divide both sides by 5

To solve for \( v \), we divide both sides of the equation \( 5v = 40 \) by 5. That is \( \frac{5v}{5} = \frac{40}{5} \), which gives us \( v = 8 \).

Answer:

\( v = 8 \)