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Solve log(0.2). (x+2)/x le 1....

Solve ` log_(0.2). (x+2)/x le 1`.

Text Solution

Verified by Experts

The correct Answer is:
`x in (-infty, -5/2] cup(0, + infty)`
`(x+2)/x ge (0.2)^(1)`
` rArr (x+2)/x ge 1/5`
Multiplying by ` 5x^(2)` (positive), we get
` 5x (x+2) ge x^(2) or 4x^(2) + 10x ge 0`
` rArr x ge0 or x le - 5/2`
Also,`(x+2)/x gt 0`
` rArr x(x+2) gt 0`
`rArr x lt -2 or x gt 0`
Therefore, the solution set is `(-infty, - 5/2] cup (0, + infty)`.
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