What is 1<= |3-2x|<5 ?

The solution to 1<= |3-2x|<5 is -1<x<= 1\lor 2<= x<4

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1<= |3-2x|<5

1 \leq ∣ 3 - 2 x ∣ < 5

- 1 < x \leq 1 or 2 \leq x < 4

Interval Notation

(- 1, 1] \cup [2, 4)

Solution steps

1 \leq ∣ 3 - 2 x ∣ < 5

a \leq u < b

then

a \leq u and u < b

1 \leq ∣ 3 - 2 x ∣ and ∣ 3 - 2 x ∣ < 5

1 \leq ∣ 3 - 2 x ∣ : x \leq 1 or x \geq 2

∣ 3 - 2 x ∣ < 5 : - 1 < x < 4

Combine the intervals

(x \leq 1 or x \geq 2) and - 1 < x < 4

Merge Overlapping Intervals

- 1 < x \leq 1 or 2 \leq x < 4

\frac{1}{8} + \frac{1}{8}

f (g (1))

(11 - 2 x) (5 - 2 x) \geq 0

2 x - 5 > - 11 or - 10 x - 6 \geq 44

i^{27}