To solve the compound inequalities \( f + 8 \leq 4 \) and \( 2f - 7 > 13 \), we will solve each inequality separately.
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Solve \( f + 8 \leq 4 \):
Subtract 8 from both sides:
\[ f \leq 4 - 8 \] \[ f \leq -4 \]
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Solve \( 2f - 7 > 13 \):
Add 7 to both sides:
\[ 2f > 13 + 7 \] \[ 2f > 20 \]
Now, divide both sides by 2:
\[ f > \frac{20}{2} \] \[ f > 10 \]
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Combine the solutions:
The solution to the compound inequality is:
\[ f \leq -4 \quad \text{or} \quad f > 10 \]
In interval notation, this can be expressed as:
\[ (-\infty, -4] \cup (10, \infty) \]
In terms of integers, the solution can be represented as:
\[ f \in { \ldots, -6, -5, -4 } \quad \text{or} \quad f \in {11, 12, 13, \ldots} \]
So the final answer in terms of integers is:
\[ f \leq -4 \quad \text{or} \quad f > 10 \]