To solve the compound inequality
\[ -1 \leq \frac{h + 15}{4} \leq 4, \]
we can break it into two separate inequalities. We will solve both inequalities step by step.
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First Inequality: \[ -1 \leq \frac{h + 15}{4} \]
Multiply both sides by 4 (note that multiplying by a positive number does not change the inequality direction): \[ -4 \leq h + 15 \]
Subtract 15 from both sides: \[ -4 - 15 \leq h \] \[ -19 \leq h \quad \text{or} \quad h \geq -19 \]
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Second Inequality: \[ \frac{h + 15}{4} \leq 4 \]
Again, multiply both sides by 4: \[ h + 15 \leq 16 \]
Subtract 15 from both sides: \[ h \leq 16 - 15 \] \[ h \leq 1 \]
Now, we combine the results from both inequalities. We have:
\[ -19 \leq h \leq 1 \]
Therefore, the solution as a compound inequality with integers is:
\[ -19 \leq h \leq 1. \]