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Popular >

| 1/X+3|<= 4

Solution

\frac{1}{X} + 3 \leq 4

Solution

X \leq - \frac{1}{7} or X \geq 1

+2

Interval Notation

(- \infty, - \frac{1}{7}] \cup [1, \infty)

Decimal Notation

X \leq - 0.14285 \dots or X \geq 1

Solution steps

\frac{1}{X} + 3 \leq 4

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 4 \leq \frac{1}{X} + 3 \leq 4

\frac{1}{X} + 3 \geq - 4 and \frac{1}{X} + 3 \leq 4

(X \leq - \frac{1}{7} or X > 0) and (X < 0 or X \geq 1)

Merge Overlapping Intervals

X \leq - \frac{1}{7} or X \geq 1

Popular Examples

∣ 2 s - 7 ∣ \geq - 1

n^{2} = 49

factor \sqrt[5]{32+8i}factor

(x-6)^2+2(x-6)-8=0

(x - 6)^{2} + 2 (x - 6) - 8 = 0

∣ 2 x - 3 ∣ < 7

Frequently Asked Questions (FAQ)

What is | 1/X+3|<= 4 ?
The solution to | 1/X+3|<= 4 is X<=-1/7 \lor X>= 1