Answer:
Explanation:
Let's solve the inequality and then graph the solution on the number line.
Starting with the inequality:
\[4x + 7 \geq -13\]
Subtract 7 from both sides:
\[4x \geq -20\]
Divide both sides by 4 (note: since 4 is positive, we don't need to flip the inequality sign):
\[x \geq -5\]
Now, the second part of the inequality:
\[15 \geq 4x + 7\]
Subtract 7 from both sides:
\[8 \geq 4x\]
Divide both sides by 4:
\[2 \geq x\]
So, the solution to the system of inequalities is \(x \geq -5\) and \(2 \geq x\).
Now, let's graph this on the number line:
```
<--------[=======]------------------|
-5 2
```
The square bracket at -5 indicates that -5 is included in the solution (greater than or equal to), and the parenthesis at 2 indicates that 2 is not included in the solution (greater than, not equal to). The shaded region represents the values of \(x\) that satisfy the inequalities.