Question

Solve the inequality:

Answer 1

Answer:

8 - 2x <4 gives us x>2

|x-8| >22 gives us (-inf, -14) and (30,inf)

|x+5| < 4 gives us (-9,-1)

Step-by-step explanation:

Inequalities differs from equalities in that they return a range of values for x and not a single value (case of equalities)

The first one

8 - 2x <4 if you subtract every side 8, you will get -2x<-4

Next divide every side with -2, since its a negative number you have to change the orientation of the inequaiity, thus we have x>4/2, x>2

The second

|x-8| >22, it has to be treated as this. -22>x-2>22 which can be treated as two single inequalities, -22>x-8, and the other, x-8>22. The fist gives you x<-14, and the other x>30, two non intercepting ranges, so your range will be (-inf, -14) and (30, inf)

The third

|x+5| < 4 if you apply the same steps from above, you will have the following  -4<x+5<4 This results in two intercepting ranges, giving you the range (-9,-1)