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Popular >

|(x-1)/(x+2)|<= 4

Solution

\frac{x - 1}{x + 2} \leq 4

Solution

x \leq - 3 or x \geq - \frac{7}{5}

+2

Interval Notation

(- \infty, - 3] \cup [- \frac{7}{5}, \infty)

Decimal Notation

x \leq - 3 or x \geq - 1.4

Solution steps

\frac{x - 1}{x + 2} \leq 4

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 4 \leq \frac{x - 1}{x + 2} \leq 4

\frac{x - 1}{x + 2} \geq - 4 and \frac{x - 1}{x + 2} \leq 4

(x < - 2 or x \geq - \frac{7}{5}) and (x \leq - 3 or x > - 2)

Merge Overlapping Intervals

x \leq - 3 or x \geq - \frac{7}{5}

Popular Examples

factor 2x^3-x^2+2x-1 factor

2 x^{3} - x^{2} + 2 x - 1

simplify 1/2*20 simplify

\frac{1}{2} \cdot 20

5 (0) - 6 y = 60

factor 3s^3+9s^2 factor

3 s^{3} + 9 s^{2}

simplify sqrt(24)+sqrt(54)-sqrt(6)simplify

24 + 54 - 6

Frequently Asked Questions (FAQ)

What is |(x-1)/(x+2)|<= 4 ?
The solution to |(x-1)/(x+2)|<= 4 is x<=-3\lor x>=-7/5