Question

-9 > -\frac{1}{3}w + 6

Explanation:

Step1: Subtract 6 from both sides

To isolate the term with \( w \), we subtract 6 from both sides of the inequality \( 9 > -\frac{1}{3}w + 6 \). This gives us \( 9 - 6 > -\frac{1}{3}w + 6 - 6 \), which simplifies to \( 3 > -\frac{1}{3}w \).

Step2: Multiply both sides by -3 (and reverse inequality)

Now, we multiply both sides of the inequality \( 3 > -\frac{1}{3}w \) by -3. When multiplying or dividing an inequality by a negative number, we must reverse the inequality sign. So, \( 3 \times (-3) < -\frac{1}{3}w \times (-3) \), which simplifies to \( -9 < w \), or equivalently \( w > -9 \).

Answer:

\( w > -9 \)