What is 0<|x-5|< 1/2 ?

The solution to 0<|x-5|< 1/2 is 9/2 <x<5\lor 5<x< 11/2

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0<|x-5|< 1/2

0 < ∣ x - 5 ∣ < \frac{1}{2}

\frac{9}{2} < x < 5 or 5 < x < \frac{11}{2}

Interval Notation

(\frac{9}{2}, 5) \cup (5, \frac{11}{2})

Decimal Notation

4.5 < x < 5 or 5 < x < 5.5

Solution steps

0 < ∣ x - 5 ∣ < \frac{1}{2}

a < u < b

then

a < u and u < b

0 < ∣ x - 5 ∣ and ∣ x - 5 ∣ < \frac{1}{2}

0 < ∣ x - 5 ∣ : x < 5 or x > 5

∣ x - 5 ∣ < \frac{1}{2} : \frac{9}{2} < x < \frac{11}{2}

Combine the intervals

(x < 5 or x > 5) and \frac{9}{2} < x < \frac{11}{2}

Merge Overlapping Intervals

\frac{9}{2} < x < 5 or 5 < x < \frac{11}{2}

\frac{7}{8} + \frac{5}{8}

\frac{1}{2} + 4

s^{2} + 7 s = - 15

\frac{5 π}{4} \cdot \frac{180}{π}

5 x - 3 (2 x - 6) - 3 (x + 2) = 2 x - 6