What is 1/(|x-3|)>= 4 ?

The solution to 1/(|x-3|)>= 4 is 11/4 <= x<3\lor 3<x<= 13/4

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1/(|x-3|)>= 4

\frac{1}{∣ x - 3 ∣} \geq 4

\frac{11}{4} \leq x < 3 or 3 < x \leq \frac{13}{4}

Interval Notation

[\frac{11}{4}, 3) \cup (3, \frac{13}{4}]

Decimal Notation

2.75 \leq x < 3 or 3 < x \leq 3.25

Solution steps

\frac{1}{∣ x - 3 ∣} \geq 4

Find positive and negative intervals

x < 3, x \geq 3

Solve the inequality for each interval

\frac{11}{4} \leq x < 3 or 3 < x \leq \frac{13}{4}

x^{2} - 16 x + 53 = 0

1.75 + 1.5 m = 28.75

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

\frac{4}{∣ x ∣ + 1} \leq ∣ x ∣ + 1

49 x^{2} + 42 x + 9

What is 1/(|x-3|)>= 4 ?
The solution to 1/(|x-3|)>= 4 is 11/4 <= x<3\lor 3<x<= 13/4