we are asked to solve a system of inequalities that reads:
18 + 2 x < 12
5 x + 2 >= - 18
so we solve for x in each one:
18 + 2 x < 12
subtract 18 from boths sides:
2 x < 12 - 18
2 x < - 6
divide by 2 both sides:
x < - 3
5 x + 2 >= - 18
subtract 2 from both sides:
5 x >= - 20
divide both sides by 5:
x >= -4
so this tells us that we want x values larger than or equal to -4 and x values smaller than -3.
So, please allow me to plot these two sections and see if there is an intersection of both sets:. The graphing can take a little time, so please be patient.
Notice that we have highlighted in green the section of the number line with x-values to the RIGHT of -4 (and also including the "-4" point with a "solid dot".
On the other extreme of this segment we see an "empty dot" at the point -3 on the number line. In this case we are NOT including the value "-3" as per the inequality that asks for x numbers strictly smaller than -3 (so to the left of "-3" NOT including "-3" (represented by the empty dot.
So the graph of the compounded inequality is given above, and the mathematical way to express it is:
- 4 <= x < - 3