To solve the inequality \( w - 6 < -4 \) or \( w - 14 \geq 1 \), we will solve each inequality separately.
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Solving \( w - 6 < -4 \):
\[ w - 6 < -4 \]
To isolate \( w \), add 6 to both sides:
\[ w < -4 + 6 \] \[ w < 2 \]
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Solving \( w - 14 \geq 1 \):
\[ w - 14 \geq 1 \]
To isolate \( w \), add 14 to both sides:
\[ w \geq 1 + 14 \] \[ w \geq 15 \]
Now we combine the two solutions. The inequalities dictate that \( w \) can either be less than 2 or greater than or equal to 15.
Thus, the solution can be expressed as a compound inequality:
\[ w < 2 \quad \text{or} \quad w \geq 15 \]
In integer form, this means: \[ (-\infty, 2) \cup [15, \infty) \]
So the final solution is: \[ w < 2 \quad \text{or} \quad w \geq 15 \]
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