What is 6/(x-7)>= 3 ?

The solution to 6/(x-7)>= 3 is 7<x<= 9

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6/(x-7)>= 3

\frac{6}{x - 7} \geq 3

7 < x \leq 9

Interval Notation

(7, 9]

Solution steps

\frac{6}{x - 7} \geq 3

Rewrite in standard form

\frac{- 3 x + 27}{x - 7} \geq 0

Factor

\frac{- 3 x + 27}{x - 7} : \frac{- 3 ( x - 9 )}{x - 7}

\frac{- 3 ( x - 9 )}{x - 7} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 3 ( x - 9 ) ) ( - 1 )}{x - 7} \leq 0 \cdot (- 1)

Simplify

\frac{3 ( x - 9 )}{x - 7} \leq 0

Divide both sides by

3

\frac{\frac{3 ( x - 9 )}{x - 7}}{3} \leq \frac{0}{3}

Simplify

\frac{x - 9}{x - 7} \leq 0

Identify the intervals

7 < x \leq 9

8.99 \cdot 1 0^{9} \cdot \frac{1 \cdot 1 0 ^{- 6}}{3.01}

x^{(2)} + 24 x + 21 = 0

8^{2} + 4^{3} \cdot 2^{2}

2.3 + 0.02 (x + 20) - 4.8 = - 9

4 x^{3} - 16 x^{2} + 12 x