Question: Solve the inequality for v. 6 > -\frac{8}{9}v Simplify your answer as much as possible.

Solve the inequality for v. 6 > -\frac{8}{9}v Simplify your answer as much as possible.

Solution

To solve the inequality for \( v \): Start with the given inequality: \[ 6 > \frac{8}{9}v \] Multiply both sides by the reciprocal of \(\frac{8}{9}\), which is \(\frac{9}{8}\), to isolate \( v \): \[ 6 \times \frac{9}{8} > v \] Calculate \( 6 \times \frac{9}{8} \): \[ \frac{54}{8} > v \] Simplify \(\frac{54}{8}\): \[ \frac{27}{4} > v \] Thus, the solution is: \[ v < \frac{27}{4} \]