To solve the compound inequality \( 19 > 5w + 14 > 4 \), we can split it into two separate inequalities:
- \( 19 > 5w + 14 \)
- \( 5w + 14 > 4 \)
Let's solve the first inequality \( 19 > 5w + 14 \):
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Subtract 14 from both sides: \[ 19 - 14 > 5w \] \[ 5 > 5w \]
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Divide both sides by 5: \[ 1 > w \quad \text{or} \quad w < 1 \]
Now, let's solve the second inequality \( 5w + 14 > 4 \):
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Subtract 14 from both sides: \[ 5w > 4 - 14 \] \[ 5w > -10 \]
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Divide both sides by 5: \[ w > -2 \]
Now we combine the two results:
\(-2 < w < 1\)
Thus, the solution as a compound inequality in integer form is: \[ -2 < w < 1 \]
In integer form, this means: \[ w \in {-1, 0} \]
So the answer expressing the range as a compound inequality with integers is:
\(-2 < w < 1\), and the integers satisfying this are \(-1\) and \(0\).