Question

solve the inequality for v.
-17 < -42 - 5v
simplify your answer as much as possible.

Explanation:

Step1: Add 42 to both sides

To isolate the term with \( v \), we add 42 to both sides of the inequality \( -17 < -42 - 5v \).
\[
-17 + 42 < -42 - 5v + 42
\]
Simplifying both sides, we get:
\[
25 < -5v
\]

Step2: Divide both sides by -5 (and reverse inequality)

When dividing an inequality by a negative number, we must reverse the inequality sign. We divide both sides of \( 25 < -5v \) by -5.
\[
\frac{25}{-5} > \frac{-5v}{-5}
\]
Simplifying both sides, we get:
\[
-5 > v
\]
Which can also be written as \( v < -5 \).

Answer:

\( v < -5 \)