What is 0<|-x-6|< 1/2 ?

The solution to 0<|-x-6|< 1/2 is -13/2 <x<-6\lor-6<x<-11/2

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0<|-x-6|< 1/2

0 < ∣ - x - 6 ∣ < \frac{1}{2}

- \frac{13}{2} < x < - 6 or - 6 < x < - \frac{11}{2}

Interval Notation

(- \frac{13}{2}, - 6) \cup (- 6, - \frac{11}{2})

Decimal Notation

- 6.5 < x < - 6 or - 6 < x < - 5.5

Solution steps

0 < ∣ - x - 6 ∣ < \frac{1}{2}

a < u < b

then

a < u and u < b

0 < ∣ - x - 6 ∣ and ∣ - x - 6 ∣ < \frac{1}{2}

0 < ∣ - x - 6 ∣ : x < - 6 or x > - 6

∣ - x - 6 ∣ < \frac{1}{2} : - \frac{13}{2} < x < - \frac{11}{2}

Combine the intervals

(x < - 6 or x > - 6) and - \frac{13}{2} < x < - \frac{11}{2}

Merge Overlapping Intervals

- \frac{13}{2} < x < - 6 or - 6 < x < - \frac{11}{2}

t^{3} + t^{2} - 2 t

(2 x + 7)^{2} = 64

4 0^{2} + 9^{2} = x^{2}

\frac{10 !}{2 ! ( 10 - 2 ) !}

(- 125 x^{- 6})^{\frac{1}{3}}

What is 0<|-x-6|< 1/2 ?
The solution to 0<|-x-6|< 1/2 is -13/2 <x<-6\lor-6<x<-11/2