What is -8/3 <(8x+3)/9 <= 1/3 ?

The solution to -8/3 <(8x+3)/9 <= 1/3 is -27/8 <x<= 0

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-8/3 <(8x+3)/9 <= 1/3

- \frac{8}{3} < \frac{8 x + 3}{9} \leq \frac{1}{3}

- \frac{27}{8} < x \leq 0

Interval Notation

(- \frac{27}{8}, 0]

Decimal Notation

- 3.375 < x \leq 0

Solution steps

- \frac{8}{3} < \frac{8 x + 3}{9} \leq \frac{1}{3}

a < u \leq b

then

a < u and u \leq b

- \frac{8}{3} < \frac{8 x + 3}{9} and \frac{8 x + 3}{9} \leq \frac{1}{3}

- \frac{8}{3} < \frac{8 x + 3}{9} : x > - \frac{27}{8}

\frac{8 x + 3}{9} \leq \frac{1}{3} : x \leq 0

Combine the intervals

x > - \frac{27}{8} and x \leq 0

Merge Overlapping Intervals

- \frac{27}{8} < x \leq 0

x^{2} + 20 x + 64 = 0

∣ 3 x - 9 ∣ < 18

x^{2} + 10 x + 2 = 0

3^{2} \cdot 3^{- 5}

24 3^{\frac{2}{5}}

What is -8/3 <(8x+3)/9 <= 1/3 ?
The solution to -8/3 <(8x+3)/9 <= 1/3 is -27/8 <x<= 0