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Popular >

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

Solution

\frac{∣ x + 1 ∣}{x - 1} \leq 2

Solution

x < 1

+1

Interval Notation

(- \infty, 1)

Solution steps

\frac{∣ x + 1 ∣}{x - 1} \leq 2

Move

2

to the left side

\frac{∣ x + 1 ∣}{x - 1} - 2 \leq 0

∣ x + 1 ∣ \geq 0

If

\frac{a}{b} \leq 0 and a \geq 0

then

b < 0 or a = 0

x - 1 < 0 or ∣ x + 1 ∣ = 0

x - 1 < 0 : x < 1

∣ x + 1 ∣ = 0 : x = - 1

Combine the intervals

x < 1 or x = - 1

Merge Overlapping Intervals

x < 1

Popular Examples

5 + \frac{x}{2} = 2 + x

-2(2x+1)=2(-3x+1)

- 2 (2 x + 1) = 2 (- 3 x + 1)

factor 7x^2-34x-5 factor

7 x^{2} - 34 x - 5

ln ∣ x ∣ = 1

∣ 7 x + 5 ∣ = ∣ 3 x + 13 ∣

Frequently Asked Questions (FAQ)

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