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Popular >

|(2-x)/(3+x)|<4

Solution

\frac{2 - x}{3 + x} < 4

Solution

x < - \frac{14}{3} or x > - 2

+2

Interval Notation

(- \infty, - \frac{14}{3}) \cup (- 2, \infty)

Decimal Notation

x < - 4.66666 \dots or x > - 2

Solution steps

\frac{2 - x}{3 + x} < 4

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 4 < \frac{2 - x}{3 + x} < 4

\frac{2 - x}{3 + x} > - 4 and \frac{2 - x}{3 + x} < 4

(x < - \frac{14}{3} or x > - 3) and (x < - 3 or x > - 2)

Merge Overlapping Intervals

x < - \frac{14}{3} or x > - 2

Popular Examples

4 (x - 5) + 2 = x + 3

simplify 7ln(1/2)+5ln(2)simplify

7 ln (\frac{1}{2}) + 5 ln (2)

(x + 5)^{2} = - 9

simplify (x^{2/3})^{3/4}simplify

(x^{\frac{2}{3}})^{\frac{3}{4}}

∣ - 2 x + 3 ∣ \leq 17

Frequently Asked Questions (FAQ)

What is |(2-x)/(3+x)|<4 ?
The solution to |(2-x)/(3+x)|<4 is x<-14/3 \lor x>-2