What is 2-9|p+7|>-16 ?

The solution to 2-9|p+7|>-16 is -9<p<-5

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2-9|p+7|>-16

2 - 9 ∣ p + 7 ∣ > - 16

- 9 < p < - 5

Interval Notation

(- 9, - 5)

Solution steps

2 - 9 ∣ p + 7 ∣ > - 16

Move

2

to the right side

- 9 ∣ p + 7 ∣ > - 18

Multiply both sides by

- 1

9 ∣ p + 7 ∣ < 18

Divide both sides by

9

∣ p + 7 ∣ < 2

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 2 < p + 7 < 2

p + 7 > - 2 and p + 7 < 2

p > - 9 and p < - 5

Merge Overlapping Intervals

- 9 < p < - 5

\frac{x}{- 3} - 20 < - 25

(\frac{k ( k + 1 )}{2})^{2}

y^{2} - 14 y + 49 = - 4

- 5 + 1

3 x^{2} + 24 = 18 x