What is |2+5/x |>= 1 ?

The solution to |2+5/x |>= 1 is x 0

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|2+5/x |>= 1

2 + \frac{5}{x} \geq 1

x \leq - 5 or - \frac{5}{3} \leq x < 0 or x > 0

Interval Notation

(- \infty, - 5] \cup [- \frac{5}{3}, 0) \cup (0, \infty)

Decimal Notation

x \leq - 5 or - 1.66666 \dots \leq x < 0 or x > 0

Solution steps

2 + \frac{5}{x} \geq 1

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

u \geq a

2 + \frac{5}{x} \leq - 1 or 2 + \frac{5}{x} \geq 1

2 + \frac{5}{x} \leq - 1 or 2 + \frac{5}{x} \geq 1

- \frac{5}{3} \leq x < 0 or (x \leq - 5 or x > 0)

Merge Overlapping Intervals

x \leq - 5 or - \frac{5}{3} \leq x < 0 or x > 0

- 2 \leq x < 1

- (3 - 4 x) + 2 \cdot (x - 1) = 6 \cdot (x + 8)

- 3 m^{2} n^{2} + 8 m n^{3} + m^{3} n

5 x^{2} - 17 x + 6

\frac{1}{3} (6)

What is |2+5/x |>= 1 ?
The solution to |2+5/x |>= 1 is x<=-5\lor-5/3 <= x<0\lor x>0