Answer :

Sure, let's solve the inequality \( -8 \leq 8 + y \) step by step and graph the solution.

Step 1: Isolate the variable \( y \).

The inequality is given as:
[tex]\[ -8 \leq 8 + y \][/tex]

To isolate \( y \), subtract 8 from both sides of the inequality:
[tex]\[ -8 - 8 \leq y \][/tex]

Step 2: Simplify the inequality.

When you simplify the left side:
[tex]\[ -16 \leq y \][/tex]

This can be rewritten as:
[tex]\[ y \geq -16 \][/tex]

Step 3: Graph the solution.

To graph \( y \geq -16 \), follow these steps:

1. Draw a number line.

2. Locate -16 on the number line.

3. Shade the region to the right of -16, indicating all numbers greater than or equal to -16.

4. Put a closed circle on -16 to show that -16 is included in the solution set.

Here is what the graph looks like:

[tex]\[ \begin{array}{c} \text{------•=========} \\ \text{ -16 } \end{array} \][/tex]

The shaded portion of the number line starts at -16 and extends to the right, covering all values greater than or equal to -16.

In summary, the solution to the inequality [tex]\( -8 \leq 8 + y \)[/tex] is [tex]\( y \geq -16 \)[/tex], and the graph represents all numbers greater than or equal to -16.