Question

solve for a and graph the solution.
8 ≥ a - 2 ≥ -6
plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.
number line with -4, -2, 0, 2, 4, 6, 8, 10, 12

Explanation:

Step1: Add 2 to all parts

To solve the compound inequality \(8 \geq a - 2 \geq -6\), we add 2 to each part of the inequality. This is done to isolate the variable \(a\).
\[
8 + 2 \geq a - 2 + 2 \geq -6 + 2
\]

Step2: Simplify each part

Simplify the left, middle, and right parts of the inequality.
\[
10 \geq a \geq -4
\]
Which can also be written as \(-4 \leq a \leq 10\).

For graphing: The solution is all real numbers between \(-4\) and \(10\), including both endpoints. So on the number line, we plot closed circles at \(-4\) and \(10\) and draw a line segment connecting them.

Answer:

The solution for \(a\) is \(-4 \leq a \leq 10\). For the graph, plot closed circles at \(-4\) and \(10\) and connect them with a line segment.