Answer:
see attached
Explanation:
In general, you plot the solution to an inequality by placing a dot at the bound, then extending a line in the direction indicated by the inequality.
If the inequality symbol is < or >, the dot will be an open circle.
If the inequality symbol is ≤ or ≥, the dot will be a solid dot. That is the kind of dot needed here.
The boundary (dot) location for x ≥ -8 is at -8 on the number line. The inequality indicates that values of x greater than that are in the solution set, so the line will be shaded to the right of the dot.
The boundary (dot) location for x ≤ -2 is at -2 on the number line. The inequality indicates that values of x less than that are in the solution set, so the line will be shaded to the left of this dot.
Since the values of x must satisfy both inequalities (the conjunction is "and"), the solution set is where the lines overlap—between -8 and -2 on the number line.
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Additional comment
I find it useful to write inequalities with the "arrow" pointing to the left. Here, the inequalities would be written ...
-8 ≤ x and x ≤ -2
Note that x is in the middle when the far left number is less than the far right number. (-8 < -2). That means, the inequality can be written as the compound ...
-8 ≤ x ≤ -2
When the inequalities are written in this way, with arrow(s) pointing left, the location of the variable relative to the constant is the location of the shaded line relative to the dot representing the constant. Here, the appearance of ...
-8 ≤ x ≤ -2
effectively shows you that the number line is shaded between solid dots at -8 and -2.