What is 2<= |2x-1|<= 10 ?

The solution to 2<= |2x-1|<= 10 is -9/2 <= x<=-1/2 \lor 3/2 <= x<= 11/2

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2<= |2x-1|<= 10

2 \leq ∣ 2 x - 1 ∣ \leq 10

- \frac{9}{2} \leq x \leq - \frac{1}{2} or \frac{3}{2} \leq x \leq \frac{11}{2}

Interval Notation

[- \frac{9}{2}, - \frac{1}{2}] \cup [\frac{3}{2}, \frac{11}{2}]

Decimal Notation

- 4.5 \leq x \leq - 0.5 or 1.5 \leq x \leq 5.5

Solution steps

2 \leq ∣ 2 x - 1 ∣ \leq 10

a \leq u \leq b

then

a \leq u and u \leq b

2 \leq ∣ 2 x - 1 ∣ and ∣ 2 x - 1 ∣ \leq 10

2 \leq ∣ 2 x - 1 ∣ : x \leq - \frac{1}{2} or x \geq \frac{3}{2}

∣ 2 x - 1 ∣ \leq 10 : - \frac{9}{2} \leq x \leq \frac{11}{2}

Combine the intervals

(x \leq - \frac{1}{2} or x \geq \frac{3}{2}) and - \frac{9}{2} \leq x \leq \frac{11}{2}

Merge Overlapping Intervals

- \frac{9}{2} \leq x \leq - \frac{1}{2} or \frac{3}{2} \leq x \leq \frac{11}{2}

2 > 2 x > 10

x + 1 > 3 > 5 - 2 x

- 3 < - \frac{1}{2} - 2 \frac{x}{3} \leq \frac{5}{6}

2 \leq ∣ x - 3 ∣ \leq 6

- 6 \leq [x] < 1

What is 2<= |2x-1|<= 10 ?
The solution to 2<= |2x-1|<= 10 is -9/2 <= x<=-1/2 \lor 3/2 <= x<= 11/2