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Popular >

2/x-3<= 5

Solution

\frac{2}{x} - 3 \leq 5

Solution

x < 0 or x \geq \frac{1}{4}

+2

Interval Notation

(- \infty, 0) \cup [\frac{1}{4}, \infty)

Decimal Notation

x < 0 or x \geq 0.25

Solution steps

\frac{2}{x} - 3 \leq 5

Rewrite in standard form

\frac{2 - 8 x}{x} \leq 0

Factor

\frac{2 - 8 x}{x} : \frac{- 2 ( 4 x - 1 )}{x}

\frac{- 2 ( 4 x - 1 )}{x} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 2 ( 4 x - 1 ) ) ( - 1 )}{x} \geq 0 \cdot (- 1)

Simplify

\frac{2 ( 4 x - 1 )}{x} \geq 0

Divide both sides by

2

\frac{\frac{2 ( 4 x - 1 )}{x}}{2} \geq \frac{0}{2}

Simplify

\frac{4 x - 1}{x} \geq 0

Identify the intervals

x < 0 or x \geq \frac{1}{4}

Popular Examples

(x - 4)^{2} + 25 = 0

t^{2} + 7 t + 12 = 0

simplify-1+1/2 simplify

- 1 + \frac{1}{2}

5 x^{2} - 7 x = 2

simplify (42-62)/(62)simplify

\frac{42 - 62}{62}

Frequently Asked Questions (FAQ)

What is 2/x-3<= 5 ?
The solution to 2/x-3<= 5 is x<0\lor x>= 1/4