In the given problem, solve and graph. Express the answer in both inequality and interval notation. $\frac{5 x - 8}{x - 5} \geq 2$

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Solution

$\frac{5 x - 8}{x - 5} \geq 2$

$\frac{5 x - 8}{x - 5} - 2 \geq 0$

$\frac{3 x + 2}{x - 5} \geq 0$

x<- $\frac{2}{3}$

x=- $\frac{3 x + 2}{x - 5}$

- $\frac{3 x + 2}{x - 5}$ <x<5

x=5

x>5

3x+2

-

0

+

+

+

x-5

-

-

-

0

+

$\frac{3 x + 2}{x - 5}$

+

0

-

undefined

+

$⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} S o l u t i o n : & x \leq - \frac{2}{3} o r x > 5 D e c i m a l : & x \leq - 0.66667 \dots o r x > 5 I n t e r v a l N o t a t i o n : & (- \infty, - \frac{2}{3}] \cup (5, \infty) \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦$

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