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} \leq \frac{11}{6}

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

Interval Notation

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

Decimal Notation

- 2 \leq x \leq 3.75

Solution steps

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

a \leq u \leq b

then

a \leq u and u \leq b

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

Combine the intervals

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

Merge Overlapping Intervals

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

\frac{( - x + 3 )}{2 - 2} \leq \frac{( 3 ( x + 2 ) )}{5} \leq \frac{x}{6}

7 < 2 (x^{2}) + 1 \leq 19

2 x - 3 < x + 1 \leq 4 x + 7

- 8 < 5 x - 3 < 7

x - 3 < 2 (x - \frac{1}{2}) \leq x + 4

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