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

The solution to |((2-3x))/(2x+3)|<1 is -1/5 <x<5

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

\frac{( 2 - 3 x )}{2 x + 3} < 1

- \frac{1}{5} < x < 5

Solution steps

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

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

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

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

- \frac{3}{2} < x < 5 and (x < - \frac{3}{2} or x > - \frac{1}{5})

Merge Overlapping Intervals

- \frac{1}{5} < x < 5

- 4 (- 3)^{2} + 4 - (6 - 2)

10 x^{2} - 40 x - 60 = 0

\frac{1}{2} (x - \frac{1}{3}) = \frac{3}{4} - \frac{x}{6}

\frac{8 π}{6}

\frac{4 ! 6 !}{5 ! 3 !}