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$Solve for v. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. -42 v+33 < 8v+91$

Solve for $v$ . Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $\newline$ -42v + 33 < 8v + 91

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Solve multi-step inequalities

Full solution

Q. Solve for

v

. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.

\newline

-42v + 33 < 8v + 91

Step $1$ : Rearrange the terms: First, we want to get all the terms with $v$ on one side of the inequality and the constant terms on the other side. We can do this by adding $42v$ to both sides of the inequality to move the $-42v$ term to the right side. $\newline$ -42v + 33 + 42v < 8v + 91 + 42v $\newline$ This simplifies to: $\newline$ 33 < 50v + 91
Step $2$ : Isolate the term with $v$ : Next, we want to isolate the term with $v$ on one side by subtracting $91$ from both sides of the inequality to move the constant term to the left side. $\newline$ 33 - 91 < 50v + 91 - 91 $\newline$ This simplifies to: $\newline$ -58 < 50v
Step $3$ : Solve for $v$ : Now, we divide both sides of the inequality by $50$ to solve for $v$ . $\newline$ -\frac{58}{50} < \frac{50v}{50} $\newline$ This simplifies to: $\newline$ -\frac{29}{25} < v

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