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Popular >

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

Solution

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

Solution

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

+2

Interval Notation

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

Decimal Notation

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

Solution steps

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

Switch sides

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

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

or

u \geq a

\frac{3 x + 2}{x - 3} \leq - 1 or \frac{3 x + 2}{x - 3} \geq 1

\frac{3 x + 2}{x - 3} \leq - 1 or \frac{3 x + 2}{x - 3} \geq 1

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

Merge Overlapping Intervals

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

Popular Examples

(2 x + 7)^{2} = 25

∣ x + 6 ∣ = ∣ 2 x + 2 ∣

|4-1/2 w|-1/3 = 1/2

4 - \frac{1}{2} w - \frac{1}{3} = \frac{1}{2}

simplify (n^{3/5})/(n^{-3/4)}simplify

\frac{n ^{\frac{3}{5}}}{n ^{- \frac{3}{4}}}

w^{2} - 5 w + 6 = 0

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