To solve for \( w \) in the inequalities \( 3w - 16 < -1 \) and \( w - 4 \geq 13 \), we will solve each inequality separately.
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Solve \( 3w - 16 < -1 \): \[ 3w - 16 < -1 \] Add 16 to both sides: \[ 3w < 15 \] Divide by 3: \[ w < 5 \]
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Solve \( w - 4 \geq 13 \): \[ w - 4 \geq 13 \] Add 4 to both sides: \[ w \geq 17 \]
Now we can combine the results. The solution is: \[ w < 5 \quad \text{or} \quad w \geq 17 \]
Expressed as a compound inequality, the solution is: \[ (-\infty, 5) \cup [17, \infty) \]
In terms of integers, we can write the solution as: \[ w < 5 \quad \text{or} \quad w \geq 17 \]
So the final answer is: \[ w \in {..., -2, -1, 0, 1, 2, 3, 4} \quad \text{or} \quad w \in {17, 18, 19, ...} \]