To solve the inequality \( 18 > 32(4w - 4) \), let's start by simplifying the right side:
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Distribute \( 32 \): \[ 18 > 32 \cdot 4w - 32 \cdot 4 \] This simplifies to: \[ 18 > 128w - 128 \]
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Add \( 128 \) to both sides: \[ 18 + 128 > 128w \] Simplifying this gives: \[ 146 > 128w \]
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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
1 answer