What is -2< 1/2-2 x/3 < 15/6 ?

The solution to -2< 1/2-2 x/3 < 15/6 is -3<x< 15/4

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-2< 1/2-2 x/3 < 15/6

- 2 < \frac{1}{2} - 2 \frac{x}{3} < \frac{15}{6}

- 3 < x < \frac{15}{4}

Interval Notation

(- 3, \frac{15}{4})

Decimal Notation

- 3 < x < 3.75

Solution steps

- 2 < \frac{1}{2} - 2 \cdot \frac{x}{3} < \frac{15}{6}

a < u < b

then

a < u and u < b

- 2 < \frac{1}{2} - 2 \cdot \frac{x}{3} and \frac{1}{2} - 2 \cdot \frac{x}{3} < \frac{15}{6}

- 2 < \frac{1}{2} - 2 \cdot \frac{x}{3} : x < \frac{15}{4}

\frac{1}{2} - 2 \cdot \frac{x}{3} < \frac{15}{6} : x > - 3

Combine the intervals

x < \frac{15}{4} and x > - 3

Merge Overlapping Intervals

- 3 < x < \frac{15}{4}

3 < ∣ x - 4 ∣ < 4

3 < x^{2} < 5

- 2 < 4 x - 10 < 6

x < 220 < x + 1

0 < x < 30

What is -2< 1/2-2 x/3 < 15/6 ?
The solution to -2< 1/2-2 x/3 < 15/6 is -3<x< 15/4