What is 1/(|x-4|)>= 1/(x+7) ?

The solution to 1/(|x-4|)>= 1/(x+7) is x 4

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1/(|x-4|)>= 1/(x+7)

\frac{1}{∣ x - 4 ∣} \geq \frac{1}{x + 7}

x < - 7 or - \frac{3}{2} \leq x < 4 or x > 4

Interval Notation

(- \infty, - 7) \cup [- \frac{3}{2}, 4) \cup (4, \infty)

Decimal Notation

x < - 7 or - 1.5 \leq x < 4 or x > 4

Solution steps

\frac{1}{∣ x - 4 ∣} \geq \frac{1}{x + 7}

Find positive and negative intervals

x < 4, x \geq 4

Solve the inequality for each interval

x < - 7 or - \frac{3}{2} \leq x < 4 or x > 4

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

h - 10 < 4

\frac{6 - 5 x}{3} = 5 x - 2

x^{3} + 10 x^{2} + 27 x + 10

6 x^{2} + 11 x y - 10 y^{2}

What is 1/(|x-4|)>= 1/(x+7) ?
The solution to 1/(|x-4|)>= 1/(x+7) is x<-7\lor-3/2 <= x<4\lor x>4