To solve the compound inequality \(-4 \leq g + 7 \leq 14\), you can break it down into two separate inequalities:
- \(-4 \leq g + 7\)
- \(g + 7 \leq 14\)
Now, let's solve each part step by step.
For the first inequality:
\[ -4 \leq g + 7 \]
Subtract 7 from both sides:
\[ -4 - 7 \leq g \]
This simplifies to:
\[ -11 \leq g \quad \text{or} \quad g \geq -11 \]
For the second inequality:
\[ g + 7 \leq 14 \]
Subtract 7 from both sides:
\[ g \leq 14 - 7 \]
This simplifies to:
\[ g \leq 7 \]
Now, we can combine the results of both inequalities:
\[ -11 \leq g \leq 7 \]
This can also be expressed as a compound inequality:
\[ -11 \leq g \leq 7 \]
Thus, the final answer is:
\[ g \in [-11, 7] \] or written as \(-11 \leq g \leq 7\).