What is 5<= (3x+5)/(-2)<10 ?

The solution to 5<= (3x+5)/(-2)<10 is -25/3 <x<=-5

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5<= (3x+5)/(-2)<10

5 \leq \frac{3 x + 5}{- 2} < 10

- \frac{25}{3} < x \leq - 5

Interval Notation

(- \frac{25}{3}, - 5]

Decimal Notation

- 8.33333 \dots < x \leq - 5

Solution steps

5 \leq \frac{3 x + 5}{- 2} < 10

a \leq u < b

then

a \leq u and u < b

5 \leq \frac{3 x + 5}{- 2} and \frac{3 x + 5}{- 2} < 10

5 \leq \frac{3 x + 5}{- 2} : x \leq - 5

\frac{3 x + 5}{- 2} < 10 : x > - \frac{25}{3}

Combine the intervals

x \leq - 5 and x > - \frac{25}{3}

Merge Overlapping Intervals

- \frac{25}{3} < x \leq - 5

x^{2} - 8 x + 16 = 5

38 = 8 x - x + 10

x^{2} + 6 x = - 8

16 \cdot \frac{5}{2}

5 x^{2} - 15 x