Question

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

w<4
w less than 4

w>4
w greater than 4

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

w<108

Answer 1

To solve the inequality \( 18 > \frac{3}{2}(4w - 4) \), let's first simplify it step by step.

1. Distribute the \(\frac{3}{2}\) on the right side:

\[
18 > \frac{3}{2} \cdot 4w - \frac{3}{2} \cdot 4
\]

This simplifies to:

\[
18 > 6w - 6
\]

2. Next, add \(6\) to both sides to isolate the term involving \(w\):

\[
18 + 6 > 6w
\]

This simplifies to:

\[
24 > 6w
\]

3. Now, divide both sides by \(6\):

\[
\frac{24}{6} > w
\]

This gives us:

\[
4 > w
\]

or in other words:

\[
w < 4
\]

So the solution to the inequality is:

**w < 4**.