Question

Find the solution to the inequality 18>3/2(4w−4) .(1 point)
Responses

w>4
w greater than 4

w>108
w greater than Start Fraction 10 over 8 End Fraction

w<4

Answer 1

To solve the inequality \( 18 > \frac{3}{2}(4w - 4) \), follow these steps:

1. Start by distributing \(\frac{3}{2}\) on the right side:
\[
\frac{3}{2}(4w - 4) = \frac{3}{2} \cdot 4w - \frac{3}{2} \cdot 4 = 6w - 6
\]
So, the inequality becomes:
\[
18 > 6w - 6
\]

2. Next, add 6 to both sides of the inequality:
\[
18 + 6 > 6w
\]
\[
24 > 6w
\]

3. Divide both sides by 6:
\[
4 > w
\]
or
\[
w < 4
\]

Thus, the solution to the inequality is:
\[
\boxed{w < 4}
\]