What is -5|4x+5|+9>-16 ?

The solution to -5|4x+5|+9>-16 is -5/2 <x<0

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-5|4x+5|+9>-16

- 5 ∣ 4 x + 5 ∣ + 9 > - 16

- \frac{5}{2} < x < 0

Interval Notation

(- \frac{5}{2}, 0)

Decimal Notation

- 2.5 < x < 0

Solution steps

- 5 ∣ 4 x + 5 ∣ + 9 > - 16

Move

9

to the right side

- 5 ∣ 4 x + 5 ∣ > - 25

Multiply both sides by

- 1

5 ∣ 4 x + 5 ∣ < 25

Divide both sides by

5

∣ 4 x + 5 ∣ < 5

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 5 < 4 x + 5 < 5

4 x + 5 > - 5 and 4 x + 5 < 5

x > - \frac{5}{2} and x < 0

Merge Overlapping Intervals

- \frac{5}{2} < x < 0

s^{2} + 13 = 0

(3 y + 6)^{2} = 36

\frac{8 - 6 i}{3 i}

\frac{10}{3} + 4

25 x^{2} - 20 x + 3 = 0