What is -2< 1/2-2 x/3 < 11/6 ?

The solution to -2< 1/2-2 x/3 < 11/6 is -2<x< 15/4

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-2< 1/2-2 x/3 < 11/6

- 2 < \frac{1}{2} - 2 \frac{x}{3} < \frac{11}{6}

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

Interval Notation

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

Decimal Notation

- 2 < x < 3.75

Solution steps

- 2 < \frac{1}{2} - 2 \cdot \frac{x}{3} < \frac{11}{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{11}{6}

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

\frac{1}{2} - 2 \cdot \frac{x}{3} < \frac{11}{6} : x > - 2

Combine the intervals

x < \frac{15}{4} and x > - 2

Merge Overlapping Intervals

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

\frac{3 x}{5 + 2} < x + 4 \leq \frac{x}{2 + 5}

0.37 < x < 0.99

\frac{1}{2} \leq 5 - \frac{x}{2} \leq 7

1 < \frac{( 3 x - 1 )}{( 2 x + 1 )} < 2

(5 x - 1) < (x + 1)^{2} < (7 x - 3)

What is -2< 1/2-2 x/3 < 11/6 ?
The solution to -2< 1/2-2 x/3 < 11/6 is -2<x< 15/4