What is (-1)/2 <(2x+3)/5 < 3/2 ?

The solution to (-1)/2 <(2x+3)/5 < 3/2 is -11/4 <x< 9/4

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(-1)/2 <(2x+3)/5 < 3/2

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

- \frac{11}{4} < x < \frac{9}{4}

Interval Notation

(- \frac{11}{4}, \frac{9}{4})

Decimal Notation

- 2.75 < x < 2.25

Solution steps

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

a < u < b

then

a < u and u < b

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

\frac{- 1}{2} < \frac{2 x + 3}{5} : x > - \frac{11}{4}

\frac{2 x + 3}{5} < \frac{3}{2} : x < \frac{9}{4}

Combine the intervals

x > - \frac{11}{4} and x < \frac{9}{4}

Merge Overlapping Intervals

- \frac{11}{4} < x < \frac{9}{4}

∣ x + 5 ∣ \leq 8

4 \cdot 60

2 s + 4 = 5 (- 4 - 2 s)

(a \cdot b)^{2}

\frac{2}{7} + \frac{1}{4} + \frac{3}{2}

What is (-1)/2 <(2x+3)/5 < 3/2 ?
The solution to (-1)/2 <(2x+3)/5 < 3/2 is -11/4 <x< 9/4