Question

solve the inequality for w.
2w + 11 < -5w - 17
simplify your answer as much as possible.

Explanation:

Step1: Add 5w to both sides

To isolate the terms with \( w \), we add \( 5w \) to both sides of the inequality \( 2w + 11 < -5w - 17 \). This gives \( 2w + 5w + 11 < -5w + 5w - 17 \), which simplifies to \( 7w + 11 < -17 \).

Step2: Subtract 11 from both sides

Next, we subtract 11 from both sides to get the term with \( w \) alone. So, \( 7w + 11 - 11 < -17 - 11 \), which simplifies to \( 7w < -28 \).

Step3: Divide both sides by 7

Finally, we divide both sides by 7 to solve for \( w \). Dividing \( 7w < -28 \) by 7 gives \( \frac{7w}{7} < \frac{-28}{7} \), so \( w < -4 \).

Answer:

\( w < -4 \)