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

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

Interval Notation

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

Decimal Notation

- 2 < x \leq 3.75

Solution steps

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

a \leq u < b

then

a \leq u and u < b

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

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

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

Combine the intervals

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

Merge Overlapping Intervals

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

5 \leq 2 x + 1 \leq 11

2 x - 1 \leq x^{2} + 3 \leq x - 1

7 - 3 x < x - 1 \leq 2 x + 9

2 x + 3 < x + 5 < 3 x + 8

\frac{81}{2} < - \frac{1}{2} - 4 x < \frac{71}{2}

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