Question

Find the solution to the inequality 18>32(4w−4)
.(1 point)
Responses

w<108
w less than Start Fraction 10 over 8 End Fraction

w<4
w less than 4

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

w>4

Answer 1

To solve the inequality \( 18 > 32(4w - 4) \), let's start by simplifying the right side:

1. **Distribute** \( 32 \):
\[
18 > 32 \cdot 4w - 32 \cdot 4
\]
This simplifies to:
\[
18 > 128w - 128
\]

2. **Add \( 128 \) to both sides**:
\[
18 + 128 > 128w
\]
Simplifying this gives:
\[
146 > 128w
\]

3. **Divide both sides by \( 128 \)**:
\[
\frac{146}{128} > w
\]
This can be simplified. First, \( \frac{146}{128} \) can be reduced by dividing both numerator and denominator by \( 2 \):
\[
\frac{73}{64} > w
\]

So, the inequality can be rewritten as:
\[
w < \frac{73}{64}
\]

Now, let's convert \( \frac{73}{64} \) to a decimal:
\[
\frac{73}{64} \approx 1.14125
\]

This is greater than \( 1 \) but less than \( 2 \).

Looking at the provided responses:
- \( w < 4 \) is a valid option since \( \frac{73}{64} < 4 \).
- None of the other responses correctly represent the solution.

Thus, the final answer for the inequality is:
\[
w < \frac{73}{64}
\]

From the options presented, it seems there isn't an exact match for \( w < \frac{73}{64} \) or \( w < 4 \) that we derived. However, the most suitable choice regarding the value of \( w \) in the context would be:

**w < 4**