Question
Solve the inequality for \( w \). \( -3 \leq-\frac{2}{9} w-5 \) Simplify your answer as much as possible.
Ask by Ayala Burgess. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( w \leq -9 \)
Solution
To solve the inequality \( -3 \leq -\frac{2}{9}w - 5 \) for \( w \), follow these steps:
1. **Add 5 to both sides:**
\[
-3 + 5 \leq -\frac{2}{9}w
\]
\[
2 \leq -\frac{2}{9}w
\]
2. **Multiply both sides by \(-1\) to isolate the term with \( w \):**
\[
-2 \geq \frac{2}{9}w
\]
(Note that multiplying by a negative number reverses the inequality sign.)
3. **Multiply both sides by \(\frac{9}{2}\) to solve for \( w \):**
\[
-2 \times \frac{9}{2} \geq w
\]
\[
-9 \geq w
\]
Which can be rewritten as:
\[
w \leq -9
\]
**Final Answer:**
\[
w \leq -9
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve the inequality \( -3 \leq -\frac{2}{9}w - 5 \), we start by isolating \( w \). 1. Add 5 to both sides: \[ -3 + 5 \leq -\frac{2}{9}w \] Simplifying this gives: \[ 2 \leq -\frac{2}{9}w \] 2. Next, we'll multiply both sides by \( -\frac{9}{2} \). Remember that when you multiply or divide by a negative number, you must reverse the inequality sign: \[ 2 \cdot -\frac{9}{2} \geq w \] This simplifies to: \[ -9 \geq w \] or equivalently, \[ w \leq -9 \] So the solution to the inequality \( -3 \leq -\frac{2}{9}w - 5 \) is \( w \leq -9 \).
