-6≤4-6v/5

solve the inequality for v

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 hour ago

To solve the inequality \(-6 \leq 4 - \frac{6v}{5}\), follow these steps:

  1. Isolate the term with \(v\): \[ -6 - 4 \leq -\frac{6v}{5} \] This simplifies to: \[ -10 \leq -\frac{6v}{5} \]

  2. Multiply both sides by -1 (remember to reverse the inequality sign): \[ 10 \geq \frac{6v}{5} \] or \[ \frac{6v}{5} \leq 10 \]

  3. Multiply both sides by 5 to eliminate the fraction: \[ 6v \leq 50 \]

  4. Divide by 6 to solve for \(v\): \[ v \leq \frac{50}{6} \]

  5. Simplify \( \frac{50}{6} \): \[ v \leq \frac{25}{3} \quad \text{or} \quad v \leq 8.33\overline{3} \]

Thus, the solution to the inequality is: \[ v \leq \frac{25}{3} \]