Question
Solve the inequality for \( v \). \[ 12 \leq 15+v \]
Ask by Rowe Huang. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( v \geq -3 \)
Solution
To solve the inequality \( 12 \leq 15 + v \) for \( v \), follow these steps:
1. **Subtract 15 from both sides** of the inequality to isolate \( v \):
\[
12 - 15 \leq v
\]
2. **Simplify the left side**:
\[
-3 \leq v
\]
3. **Rewrite the inequality** to make it clear that \( v \) is greater than or equal to \(-3\):
\[
v \geq -3
\]
**Solution:** All real numbers \( v \) with \( v \) at least –3. In symbols, \( v ≥ −3 \).
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Simplify this solution Bonus Knowledge
To solve the inequality \( 12 \leq 15 + v \), start by isolating \( v \). Subtract 15 from both sides: \[ 12 - 15 \leq v \] This simplifies to: \[ -3 \leq v \] This means that \( v \) is greater than or equal to -3. In interval notation, this can be expressed as: \[ v \in [-3, \infty) \]
