Question

solve for v. reduce any fractions to lowest terms. dont round your answer, and dont use mixed fractions. -42v + 33 < 8v + 91

Explanation:

Step1: Subtract 8v from both sides

To isolate the variable terms, we subtract \(8v\) from both sides of the inequality \(-42v + 33 < 8v + 91\). This gives us \(-42v - 8v + 33 < 91\), which simplifies to \(-50v + 33 < 91\).

Step2: Subtract 33 from both sides

Next, we subtract 33 from both sides to isolate the term with the variable. So, \(-50v + 33 - 33 < 91 - 33\), which simplifies to \(-50v < 58\).

Step3: Divide both sides by -50 (and reverse the inequality)

When dividing an inequality by a negative number, we must reverse the inequality sign. Dividing both sides of \(-50v < 58\) by \(-50\) gives \(v > \frac{58}{-50}\), which simplifies to \(v > -\frac{29}{25}\).

Answer:

\(v > -\frac{29}{25}\)