What is 6/(|x+5|)>7 ?

The solution to 6/(|x+5|)>7 is -41/7 <x<-5\lor-5<x<-29/7

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6/(|x+5|)>7

\frac{6}{∣ x + 5 ∣} > 7

- \frac{41}{7} < x < - 5 or - 5 < x < - \frac{29}{7}

Interval Notation

(- \frac{41}{7}, - 5) \cup (- 5, - \frac{29}{7})

Decimal Notation

- 5.85714 \dots < x < - 5 or - 5 < x < - 4.14285 \dots

Solution steps

\frac{6}{∣ x + 5 ∣} > 7

Find positive and negative intervals

x < - 5, x \geq - 5

Solve the inequality for each interval

- \frac{41}{7} < x < - 5 or - 5 < x < - \frac{29}{7}

1 = 9 x^{2} + 8 x

∣ 3 x - 8 ∣ < 1

\frac{14.3}{8} (- \frac{16}{15})

9 y^{2} - 1