To solve the inequality \( 18 > 32(4w - 4) \), we first simplify the right side of the inequality.
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Distributing \( 32 \) on the right side: \[ 18 > 128w - 128 \]
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Next, we add \( 128 \) to both sides: \[ 18 + 128 > 128w \] \[ 146 > 128w \]
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Now, we divide both sides by \( 128 \) to isolate \( w \): \[ \frac{146}{128} > w \]
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We can simplify \( \frac{146}{128} \). Dividing both the numerator and the denominator by \( 2 \): \[ \frac{73}{64} > w \]
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Therefore, we have: \[ w < \frac{73}{64} \]
To convert \( \frac{73}{64} \) to a decimal, calculate it: \[ 73 \div 64 \approx 1.140625 \]
Since none of the given responses match \( \frac{73}{64} \) directly, reviewing the options you provided, \( \frac{10}{8} \) simplifies to \( 1.25 \) (which is greater than \( 1.140625 \)) and can be written as \( 1 \frac{1}{4} \).
Hence, the correct option in your choices is: w < 4
This matches since \( \frac{73}{64} \) is less than \( 4 \), meaning all \( w \) values less than \( \frac{73}{64} \) are also obviously less than \( 4 \). So we conclude: w < 4.