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Popular >

(4-x)/x <1

Solution

\frac{4 - x}{x} < 1

Solution

x < 0 or x > 2

+1

Interval Notation

(- \infty, 0) \cup (2, \infty)

Solution steps

\frac{4 - x}{x} < 1

Rewrite in standard form

\frac{4 - 2 x}{x} < 0

Factor

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

\frac{- 2 ( x - 2 )}{x} < 0

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

\frac{2 ( x - 2 )}{x} > 0

Divide both sides by

2

\frac{\frac{2 ( x - 2 )}{x}}{2} > \frac{0}{2}

Simplify

\frac{x - 2}{x} > 0

Identify the intervals

x < 0 or x > 2

Popular Examples

simplify 8^3 simplify

8^{3}

0.023=Qe^{-0.000114(11000)}

0.023 = Q e^{- 0.000114 (11000)}

5/(3x-1)-(20)/(9x^2-1)< 2/(3x-1)

\frac{5}{3 x - 1} - \frac{20}{9 x ^{2} - 1} < \frac{2}{3 x - 1}

factor x^3+2x^2 factor

x^{3} + 2 x^{2}

8 x^{2} \leq 10 x - 3

Frequently Asked Questions (FAQ)

What is (4-x)/x <1 ?
The solution to (4-x)/x <1 is x<0\lor x>2