Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( -7 < w < -2 \)
Solution
1. Start with the inequality:
\[
3 > w + 5 > -2
\]
2. Subtract \( 5 \) from all three parts of the inequality:
\[
3 - 5 > w + 5 - 5 > -2 - 5
\]
3. Simplify each part:
\[
-2 > w > -7
\]
4. Rewrite the inequality in the standard increasing order:
\[
-7 < w < -2
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To solve the compound inequality \( 3 > w + 5 > -2 \), we can break it down into two separate inequalities: 1. \( 3 > w + 5 \) 2. \( w + 5 > -2 \) Starting with the first inequality: 1. \( 3 > w + 5 \) Subtract \( 5 \) from both sides: \[ 3 - 5 > w \] This simplifies to: \[ -2 > w \] or: \[ w < -2 \] Now for the second inequality: 2. \( w + 5 > -2 \) Again, subtract \( 5 \) from both sides: \[ w > -2 - 5 \] This simplifies to: \[ w > -7 \] Now we combine the two results: \[ -7 < w < -2 \] So the solution for \( w \) is: \[ w \in (-7, -2) \] This means \( w \) can be any value between \(-7\) and \(-2\), not including those endpoints.
