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 ∣ \geq - 16

- 9 \leq p \leq - 5

Interval Notation

[- 9, - 5]

Solution steps

2 - 9 ∣ p + 7 ∣ \geq - 16

Move

2

to the right side

- 9 ∣ p + 7 ∣ \geq - 18

Multiply both sides by

- 1

9 ∣ p + 7 ∣ \leq 18

Divide both sides by

9

∣ p + 7 ∣ \leq 2

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 2 \leq p + 7 \leq 2

p + 7 \geq - 2 and p + 7 \leq 2

p \geq - 9 and p \leq - 5

Merge Overlapping Intervals

- 9 \leq p \leq - 5

15 r^{2} + 2 rs - s^{2}

\frac{1}{27} x - \frac{4}{9} = \frac{2}{3}

\frac{7}{6 x} + \frac{2 - x}{3 x y}

\frac{3}{4} x + 2 = \frac{1}{8}

2 x + 3 x + 26 = 9