To solve the inequalities:
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First inequality: \( 2w - 15 \geq 1 \)
- Add 15 to both sides: \[ 2w \geq 1 + 15 \] \[ 2w \geq 16 \]
- Divide both sides by 2: \[ w \geq 8 \]
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Second inequality: \( w + 17 < 13 \)
- Subtract 17 from both sides: \[ w < 13 - 17 \] \[ w < -4 \]
Now we combine the results of both inequalities:
- The solution to the first inequality is \( w \geq 8 \).
- The solution to the second inequality is \( w < -4 \).
Thus, the final compound inequality is: \[ w \geq 8 \quad \text{or} \quad w < -4 \]
In interval notation, this can be represented as: \[ (-\infty, -4) \cup [8, \infty) \]
In terms of integers, your answer is: \[ w \in { w : w < -4 } \quad \text{or} \quad { w : w \geq 8 } \]