v = 8
Explanation:Given:
-31 = 3v + 9 - 8v
To find:
the value of v
To determine v, we will collect like terms:
[tex]\begin{gathered} -31\text{ = 3v + 9 - 8v} \\ -31\text{ = 3v - 8v + 9} \\ -31\text{ = -5v + 9} \end{gathered}[/tex]subtract 9 from both sides:
[tex]\begin{gathered} -31\text{ - 9 = -5v + 9 - 9} \\ -40\text{ = -5v} \\ \\ divide\text{ both sides by -5:} \\ \frac{-40}{-5}\text{ = }\frac{-5v}{-5} \\ division\text{ of same signs give positive sign} \\ v\text{ = 8} \end{gathered}[/tex]