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Popular >

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

Solution

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

Solution

x < - \frac{1}{2}

+2

Interval Notation

(- \infty, - \frac{1}{2})

Decimal Notation

x < - 0.5

Solution steps

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

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

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

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

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

Merge Overlapping Intervals

x < - \frac{1}{2}

Popular Examples

(5 m + 4)^{2} = 0

z^{2} + 5 z + 2 = 0

2 x - 7 = - 17

simplify (10^{-2})/(10^{-14)}simplify

\frac{1 0 ^{- 2}}{1 0 ^{- 14}}

simplify (x^3y^5)/(x^{10)y^4}simplify

\frac{x ^{3} y ^{5}}{x ^{10} y ^{4}}

Frequently Asked Questions (FAQ)

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