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 the first inequality

The inequality $x < - 5$ represents all values of $x$ that are less than -5. We draw a vertical dotted line at $x=-5$ (dotted because the inequality is strict, $x$ cannot equal -5) and shade the region to the left of this line.

Step2: Graph the second inequality

The inequality $x\geq - 8$ represents all values of $x$ that are greater than or equal to -8. We draw a vertical solid line at $x = - 8$ (solid because the inequality includes equality, $x$ can equal -8) and shade the region to the right of this line.

Step3: Find the solution region

The solution of the system of inequalities is the intersection of the two shaded - regions. The intersection 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 $-8\leq x<-5$.