What is 0<|x-3|< 1/4 ?

The solution to 0<|x-3|< 1/4 is 11/4 <x<3\lor 3<x< 13/4

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0<|x-3|< 1/4

0 < ∣ x - 3 ∣ < \frac{1}{4}

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

Interval Notation

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

Decimal Notation

2.75 < x < 3 or 3 < x < 3.25

Solution steps

0 < ∣ x - 3 ∣ < \frac{1}{4}

a < u < b

then

a < u and u < b

0 < ∣ x - 3 ∣ and ∣ x - 3 ∣ < \frac{1}{4}

0 < ∣ x - 3 ∣ : x < 3 or x > 3

∣ x - 3 ∣ < \frac{1}{4} : \frac{11}{4} < x < \frac{13}{4}

Combine the intervals

(x < 3 or x > 3) and \frac{11}{4} < x < \frac{13}{4}

Merge Overlapping Intervals

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

2 (- 2 x + 1) - 5 x + 2 = - 23

\frac{x + 8}{3 x - 2} \geq 1

1 - \frac{8}{9}

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

1 - \frac{2}{3}