Question

-6≤4-6v/5
solve the inequality for v

Answer 1

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:
\[
v \leq \frac{25}{3}
\]