Solve the inequality:

8 - 2x <4

A. X> - 2. B. X>2. C. X6

|x-8| >22

A. X> - 30 or x< - 14

B. X> 30 or x< 14

C. X> 30 or x < 14

D. X> 30 and x < 14

|x+5| < 4

A. - 9 B. - 5 < x <4

C. - 1 < x <4

D. - 1 < x <9

8 - 2x 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 x30, 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