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.
