Question

Find the solution to the inequality 18>3/2(4w−4)
.

Answer 1

To solve the inequality \( 18 > \frac{3}{2}(4w - 4) \), we will start by simplifying the right side of the inequality.

1. Distribute \( \frac{3}{2} \) across \( (4w - 4) \):
\[
\frac{3}{2}(4w - 4) = \frac{3}{2} \cdot 4w - \frac{3}{2} \cdot 4 = 6w - 6
\]

2. Now, rewrite the inequality:
\[
18 > 6w - 6
\]

3. To isolate \( w \), first add \( 6 \) to both sides:
\[
18 + 6 > 6w \quad \Rightarrow \quad 24 > 6w
\]

4. Now, divide both sides by \( 6 \):
\[
\frac{24}{6} > w \quad \Rightarrow \quad 4 > w
\]

5. We can also express this as:
\[
w < 4
\]

Thus, the solution to the inequality \( 18 > \frac{3}{2}(4w - 4) \) is

\[
w < 4.
\]