Solve the following absolute value inequalities and write th

Solve the following absolute value inequalities and write the solution set in set notation and also in interval notation. (Hint don’t forget the two types)

a. |2x - 8| <= 16

b. |10 - 3x| > 18

Solution

a) |2x -8| < = 16

for 2x-8 >0

2x -8 <= 16

2x <=24 ----> x< =12

for 2x -8<0

-(2x -8) <=16

-2x +8 <=16

2x>=-8

x>= -4

Combining the two inequalties:

-4<=x<= 12

[ -4 , 12 ]

b) |10 -3x |> 18

for 10-3x >0

10-3x >18

3x< -8

x< -8/3

for 10-3x<0

-(10 -3x) >18

-10 +3x >18

3x>28

x>28/3

Combining the two inequalities:

x< -8/3 and x> 28/3

( - inf, -8/3) U ( 28/3 , inf)