Question
Solve the inequality for \( v \). \( -8 \leq \frac{v}{-3} \)
Ask by Carrillo Gough. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( v \leq 24 \)
Solution
To solve the inequality \( -8 \leq \frac{v}{-3} \) for \( v \), follow these steps:
1. **Understand the Inequality:**
\[
-8 \leq \frac{v}{-3}
\]
2. **Isolate \( v \):**
To isolate \( v \), multiply both sides of the inequality by \(-3\). **Important:** When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign.
3. **Multiply Both Sides by \(-3\):**
\[
-8 \times (-3) \geq v
\]
\[
24 \geq v
\]
4. **Rewrite the Inequality:**
\[
v \leq 24
\]
**Solution:**
All real numbers \( v \) that are less than or equal to 24 satisfy the inequality.
**Final Answer:**
All real numbers \( v \) that are less than or equal to 24 satisfy the inequality.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To solve the inequality \( -8 \leq \frac{v}{-3} \), we start by multiplying both sides by \(-3\). Remember that when you multiply or divide an inequality by a negative number, you must reverse the inequality sign. Thus, we have: \[ -8 \times -3 \geq v \] Calculating the left side gives: \[ 24 \geq v \] This can also be written as: \[ v \leq 24 \] So the solution to the inequality is: \[ v \leq 24 \]
