Question

solve the system of inequalities by graphing.
x < -5
x ≥ -8
select a line to change it between solid and dotted. select a region to shade it.

Explanation:

Step1: Graph \(x < - 5\)

The line \(x=-5\) is a vertical line. Since the inequality is \(x < - 5\), we draw a dotted line (because the points on \(x = - 5\) are not included in the solution set) and shade the region to the left of \(x=-5\).

Step2: Graph \(x\geq - 8\)

The line \(x = - 8\) is a vertical line. Since the inequality is \(x\geq - 8\), we draw a solid line (because the points on \(x=-8\) are included in the solution set) and shade the region to the right of \(x = - 8\).

Step3: Find the intersection

The intersection of the two - shaded regions is the solution of the system of inequalities. The solution is the region between \(x=-8\) and \(x=-5\), including \(x=-8\) but not including \(x=-5\).

Answer:

The solution of the system of inequalities is \(-8\leq x < - 5\).