What is -5<= 5-3 x/2 <= 8 ?

The solution to -5<= 5-3 x/2 <= 8 is -2<= x<= 20/3

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-5<= 5-3 x/2 <= 8

- 5 \leq 5 - 3 \frac{x}{2} \leq 8

- 2 \leq x \leq \frac{20}{3}

Interval Notation

[- 2, \frac{20}{3}]

Decimal Notation

- 2 \leq x \leq 6.66666 \dots

Solution steps

- 5 \leq 5 - 3 \cdot \frac{x}{2} \leq 8

a \leq u \leq b

then

a \leq u and u \leq b

- 5 \leq 5 - 3 \cdot \frac{x}{2} and 5 - 3 \cdot \frac{x}{2} \leq 8

- 5 \leq 5 - 3 \cdot \frac{x}{2} : x \leq \frac{20}{3}

5 - 3 \cdot \frac{x}{2} \leq 8 : x \geq - 2

Combine the intervals

x \leq \frac{20}{3} and x \geq - 2

Merge Overlapping Intervals

- 2 \leq x \leq \frac{20}{3}

2 x + 4 x < 2 + 4 x < - 8 - 2 x

(1) 2 \leq \frac{( x ^{2} - 3 x )}{2} < 5

\frac{1}{2} < [x] < \frac{7}{8}

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

3 < x + 3 < 6