What is 3<(8-3x)/5 <= 8 ?

The solution to 3<(8-3x)/5 <= 8 is -32/3 <= x<-7/3

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3<(8-3x)/5 <= 8

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

- \frac{32}{3} \leq x < - \frac{7}{3}

Interval Notation

[- \frac{32}{3}, - \frac{7}{3})

Decimal Notation

- 10.66666 \dots \leq x < - 2.33333 \dots

Solution steps

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

a < u \leq b

then

a < u and u \leq b

3 < \frac{8 - 3 x}{5} and \frac{8 - 3 x}{5} \leq 8

3 < \frac{8 - 3 x}{5} : x < - \frac{7}{3}

\frac{8 - 3 x}{5} \leq 8 : x \geq - \frac{32}{3}

Combine the intervals

x < - \frac{7}{3} and x \geq - \frac{32}{3}

Merge Overlapping Intervals

- \frac{32}{3} \leq x < - \frac{7}{3}

8 x^{2} + 3 x = 5

\frac{100 y ^{3}}{98 x y}

7 (x + 4) = 3 x + 12 + x - 5

2 x^{2} - 5 x y - 3 y^{2}

- 2 - c \geq 1