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Popular >

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

Solution

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

Solution

x < - \frac{5}{2} or \frac{1}{4} < x < 3 or x > 3

+2

Interval Notation

(- \infty, - \frac{5}{2}) \cup (\frac{1}{4}, 3) \cup (3, \infty)

Decimal Notation

x < - 2.5 or 0.25 < x < 3 or x > 3

Solution steps

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

Switch sides

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

Apply absolute rule: If

∣ u ∣ > a, a > 0

then

u < - a

or

u > a

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

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

\frac{1}{4} < x < 3 or (x < - \frac{5}{2} or x > 3)

Merge Overlapping Intervals

x < - \frac{5}{2} or \frac{1}{4} < x < 3 or x > 3

Popular Examples

x^{2} + 12 x - 27 = 0

x - 4 \geq - 3

4 x^{2} - 5 = 0

14 = 3 a + 5

- 5 + ∣ 10 - 7 v ∣ = - 5

Frequently Asked Questions (FAQ)

What is 1<|(3x+2)/(x-3)| ?
The solution to 1<|(3x+2)/(x-3)| is x<-5/2 \lor 1/4 <x<3\lor x>3