Question

solve the inequality for v. -2v - 16 < 3v + 24 simplify your answer as much as possible.

Explanation:

Step1: Add \(2v\) to both sides

To get all the \(v\) terms on one side, we add \(2v\) to both sides of the inequality. This gives us:
\(-2v - 16 + 2v < 3v + 24 + 2v\)
Simplifying both sides, the \(-2v\) and \(+2v\) on the left cancel out, and on the right we combine like terms:
\(-16 < 5v + 24\)

Step2: Subtract 24 from both sides

Next, we want to isolate the term with \(v\), so we subtract 24 from both sides:
\(-16 - 24 < 5v + 24 - 24\)
Simplifying both sides:
\(-40 < 5v\)

Step3: Divide both sides by 5

To solve for \(v\), we divide both sides of the inequality by 5:
\(\frac{-40}{5} < \frac{5v}{5}\)
Simplifying both sides gives:
\(-8 < v\)
Which can also be written as \(v > -8\)

Answer:

\(v > -8\)