Question

Solve the absolute value inequality: |5x + 3|>= 13
Answer x >= -3.2 or x <= 2
x <= -3.2 and x >= 2
x <= -3.2 or x >= 3.2
x <= -3.2 or x >= 2

Answer 1

5x+3 <= -13 and 5x + 3 >=13
5x<=-16 and 5x>=10
x<=-16/5 and x>=2
x<=-3.2 and x>=2

Answer 2

use four formulae
(1) |x|<=a then -a<= x <= +a
() |x|<a then -a < x < +a
() |x|>=a then x<= -a and x>=+a
() |x|> a then x< -a and x> +a

in place of x you can substitute a bulky expression of x..

Answer 3

Solve this one the same as the other problem. solve for x the normal way for one value. and then got back and solve for x switching the signs! ^_^

So:

5x+3 >= 13
5x >= 10
x>2

-5x-3 >= 13
-5x >=16
x<=-3.2

So your answers are x>=2 and x<=-3.2