What is 1/(|x+7|)>2 ?

The solution to 1/(|x+7|)>2 is -15/2 <x<-7\lor-7<x<-13/2

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1/(|x+7|)>2

\frac{1}{∣ x + 7 ∣} > 2

- \frac{15}{2} < x < - 7 or - 7 < x < - \frac{13}{2}

Interval Notation

(- \frac{15}{2}, - 7) \cup (- 7, - \frac{13}{2})

Decimal Notation

- 7.5 < x < - 7 or - 7 < x < - 6.5

Solution steps

\frac{1}{∣ x + 7 ∣} > 2

Find positive and negative intervals

x < - 7, x \geq - 7

Solve the inequality for each interval

- \frac{15}{2} < x < - 7 or - 7 < x < - \frac{13}{2}

(x - 6)^{2} (x + 3) > 0

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

48 \cdot 7

\frac{1.4}{2.5} = \frac{g}{25}

x^{2} - 98 = 0