interval notation

Question

Solve each inequality and give the solution in interval notation:

5-3 |2 x+8| lt -22

Answer 1

5-3 |2 x+8| < -22 <==Is this what you want to solve?

Subtract 5 from both sides,

-3 |2 x+8| < -27

Divide both sides by -3, and change the direction of "<",

|2x+8| > 9

which is equivalent to

2x+8 > 9 => x > 1/2

and

2x+8 < -9 => x< -17/2

Answer: (-oo, -17/2) U (1/2, oo)