# Solving an inequality

by Shaybay92
Tags: inequality, solving
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 P: 122 I am trying to find the domain of a square root function... To do so I have to solve the following inequality: 1/(x+1) - 4/(x-2) >= 0 This is how i attempted to solve it...: I crossmultilplied the denominator to get [(x-2) - 4(x+1)]/(x-2)(x+1) >= 0 Multiplied both sides by (x-2)(x+1) (x-2) - 4(x+1) > = 0 Expanded x - 2 -4x - 4 = 0 -3x -6 >= 0 -3(x+2) >= 0 (x+2) <= 0 <---- at this point I am not sure if i swap the sign around, I haven't been taught inequalities before... but I will swap it around anyway. x <= -2 Is this the correct answer? When I graph the entire function (sqrt of the above), I get part of the function less than -2 but also part greater than -2.... I dont really understand how there can be x > -2 if I got this restriction here of >-2.
 HW Helper P: 6,202 When dealing with an inequality, if you multiply by a negative number, the inequality changes. You can deal with this by multiplying by the square of the denominator i.e. ((x+1)(x-2))2
 P: 61 Yeah, when I calculate it I get the same answer: x <= (-2)
 Mentor P: 21,249 Solving an inequality Just as rock.freak667 said, multiply both sides by (x+1)2(x-2)2. The domain is not just x <= -2.

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