What is (10)/(x-2)>= 2 ?

The solution to (10)/(x-2)>= 2 is 2<x<= 7

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(10)/(x-2)>= 2

\frac{10}{x - 2} \geq 2

2 < x \leq 7

Interval Notation

(2, 7]

Solution steps

\frac{10}{x - 2} \geq 2

Rewrite in standard form

\frac{- 2 x + 14}{x - 2} \geq 0

Factor

\frac{- 2 x + 14}{x - 2} : \frac{- 2 ( x - 7 )}{x - 2}

\frac{- 2 ( x - 7 )}{x - 2} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 2 ( x - 7 ) ) ( - 1 )}{x - 2} \leq 0 \cdot (- 1)

Simplify

\frac{2 ( x - 7 )}{x - 2} \leq 0

Divide both sides by

2

\frac{\frac{2 ( x - 7 )}{x - 2}}{2} \leq \frac{0}{2}

Simplify

\frac{x - 7}{x - 2} \leq 0

Identify the intervals

2 < x \leq 7

\frac{x ^{2} + 4 x}{x ^{2} - 36} \leq 0

\frac{1}{27} x^{12} + \frac{8}{125} y^{18}

\frac{12}{52} \cdot \frac{4}{52}

46 x + 23 = 46 x + 23

7 - ∣ 2 x - 3 ∣ = 4