The solution to (10)/x >4 is 0<x< 5/2

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(10)/x >4

Solution

\frac{10}{x} > 4

0 < x < \frac{5}{2}

Interval Notation

(0, \frac{5}{2})

Decimal Notation

0 < x < 2.5

Solution steps

\frac{10}{x} > 4

Rewrite in standard form

\frac{10 - 4 x}{x} > 0

Factor

\frac{10 - 4 x}{x} : \frac{- 2 ( 2 x - 5 )}{x}

\frac{- 2 ( 2 x - 5 )}{x} > 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 2 ( 2 x - 5 ) ) ( - 1 )}{x} < 0 \cdot (- 1)

Simplify

\frac{2 ( 2 x - 5 )}{x} < 0

Divide both sides by

2

\frac{\frac{2 ( 2 x - 5 )}{x}}{2} < \frac{0}{2}

Simplify

\frac{2 x - 5}{x} < 0

Identify the intervals

0 < x < \frac{5}{2}

t - 13 \geq 20

4 \leq 4 - x \leq 6

\frac{2 ^{n}}{2 ^{n + 1}}

\frac{52 !}{( 52 - 5 ) ! 5 !}

2 x^{3} + 5 x^{2} - 12 x