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}

11 x^{2} + 55 x = 0

\frac{1}{2} r - 3 = 3 (4 - \frac{3}{2} r)

\frac{39}{- 13}

∣ x + 7 ∣ < 0.03

x^{3} - 9 x^{2} + 24 x - 16

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