What is -3<-1/2-2 x/3 <= 5/6 ?

The solution to -3<-1/2-2 x/3 <= 5/6 is -2<= x< 15/4

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-3<-1/2-2 x/3 <= 5/6

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

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

Interval Notation

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

Decimal Notation

- 2 \leq x < 3.75

Solution steps

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

a < u \leq b

then

a < u and u \leq b

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

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

- \frac{1}{2} - 2 \cdot \frac{x}{3} \leq \frac{5}{6} : x \geq - 2

Combine the intervals

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

Merge Overlapping Intervals

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

2 \leq ∣ x - 3 ∣ \leq 6

- 6 \leq [x] < 1

5 x - 11 \leq 7 x - 5 < 9

7 x + 2 < 2 x + 3 < x - 1

13 < 3 x + 10 < 16

What is -3<-1/2-2 x/3 <= 5/6 ?
The solution to -3<-1/2-2 x/3 <= 5/6 is -2<= x< 15/4