The correct option is A [ 23,5] ∪ [5,∞] R.E.F image #160;Given inequality #160; 5x 8x 5≥ 2 obviously x≠ 5 5x 8≥ 2(x 5) 5x 8≥ 2x 10 ...

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Integration of Trigonometric Functions

5x-8 / x-5 ≥ ...

Question

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

[- \frac{2}{3}, 5] \cup [5, \infty]

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(- \infty, - \frac{2}{3}] \cup (5, \infty)

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[- \frac{2}{3}, 5)

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None of these

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Solution

The correct option is A $[- \frac{2}{3}, 5] \cup [5, \infty]$
R.E.F image
Given inequality
$\frac{5 x - 8}{x - 5} \geq 2$
obviously $x \neq 5$
$5 x - 8 \geq 2 (x - 5)$
$5 x - 8 \geq 2 x - 10$
$3 x + 2 \geq 0$
$x ϵ [\frac{- 2}{3}, 5) \cup (5, \infty)$

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