MATH III

Inequalities with absolut value

 

Smaller than |x| < k

 

2|1+4x|-15 < 3

2|1+4x| < 18

-9 < 1+4x < 9

-10 < 4x < 8

-5/2 < x < 2

(-5/2, 2)

 

|x| < -k NO SOLUTION

 

 

Greater than |x| > k

 

4 |5+2x| -14 > 2

4 |5+2x| > 16

-4 > 5+2x > 4

-9 > 2x > -1

-9/2 > x > -1/2

 

(-∞, -9/2) U (-1/2, ∞)

 

|x|> -k ALL SOLUTIONS