1<|2x-5|<8

The solution to 1<|2x-5|<8 is -3/2 <x<2\lor 3<x< 13/2

Solution

1 < ∣ 2 x - 5 ∣ < 8

- \frac{3}{2} < x < 2 or 3 < x < \frac{13}{2}

Interval Notation

(- \frac{3}{2}, 2) \cup (3, \frac{13}{2})

Decimal Notation

- 1.5 < x < 2 or 3 < x < 6.5

Solution steps

1 < ∣ 2 x - 5 ∣ < 8

a < u < b

then

a < u and u < b

1 < ∣ 2 x - 5 ∣ and ∣ 2 x - 5 ∣ < 8

1 < ∣ 2 x - 5 ∣ : x < 2 or x > 3

∣ 2 x - 5 ∣ < 8 : - \frac{3}{2} < x < \frac{13}{2}

Combine the intervals

(x < 2 or x > 3) and - \frac{3}{2} < x < \frac{13}{2}

Merge Overlapping Intervals

- \frac{3}{2} < x < 2 or 3 < x < \frac{13}{2}

12 x^{3} - 60 x^{2} + 48 x

\frac{- \frac{9 x}{x + y}}{\frac{y}{x ^{2}}}

- 8 = 16 - 2 n

7 x + 2 > - 4 (x + 5)

- 5 (x - 3) \leq 30