Futuristic wrote:

Zooroopa wrote:

The expression reduces to x^^2+2x-8>=0

This could be further reduced to (x - 4)(x + 2) >=0

Since it is a inequality please check both the expressions in the parantheses. They can be both greater than zero or both less than zero.

You should get x >=4 or x <=-2.

With all due respect, this approach seems flawed. You would need to consider the denominator as well, and values for which it becomes 0. The equation actually reduces to {[(x-4)(x+2)]/[(x+3)(x-2)]} >= 0. I know from this that we can get ranges of x.
Your approach is correct.

{[(x-4)(x+2)]/[(x+3)(x-2)]} >= 0

This basically means that we have the following ranges of values for x

(-infinity, -3) (-3,-2) (-2,2) (2,4) (4, infinity)

Now pick a vaue from each range and verify if the expression makes sense:

For eg: Range (-infinity, -3). Pick x = -4

(-4-4)(-4+2)/(-4+3)(-4-2) = (-16)*(-2)/(-1)*(2) = -16 which <=0. Hence

x has values in the range to (-infinity, -3) or

x < -3
Similarly you can verify for the other 4 ranges. You will see that some of them don't satisfy the inequality.

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