What is absolute value (4x plus 9) greater than -2?

Answer 1

|4x + 9|> -2

There are two inequalities to be solved.

4x + 9 > -2 and -(4x + 9) > -2

4x + 9 > -2

Subtract 9 from both sides.

4x > -2 - 9

4x > -11

Divide both sides by 4.

x > -11/4

-4x-9 > -2

Add 9 to both sides.

-4x > -2 + 9

-4x > 7

Divide both sides by -4. This will reverse the inequality.

x < -7/4

Solutions for x

x > -11/4

x < -7/4

Since x>-11/4 and x<-7/4 overlap, all values for x are valid answers.

Answer 2

As absolute value is always ≥ 0, |4x + 9| is always ≥ 0 > -2

Therefore |4x + 9| > -2 is true for all x.

Answer 3

It is the equation |4x + 9| > -2, which is true for all x.