INTRODUCTORY EXERCISES-Inequalities

(2) Solve each inequality.

 (a) (x + 3)(x - 4)  0

 (b) 9/4  x2

 (c) 3x2 - 2x - 6  2x2 - 6x - 1

 (d) x - 2
     ------  0
     2x + 5

 (e)   2x
     ------  0
     x2 + 5
HINT: If the inequality isn't already factored, with 0 on one side of the inequality, then manipulate the expression so that that is the situation.

Then, note that the sign of each factor determines the sign of the product (or in the case of a quotient, the sign of the factors of the numerator and denominator).

So for example, in question (a), if the product is to be positive (forget about the equals sign for a moment), then either x+3 and x-4 must be positive, or both must be negative. You should be able to determine when x+3> 0 and x-4 > 0; then when x+3 < 0 and x-4 < 0. (Eventually you should obtain two non-overlapping intervals.) Then note that the product equals 0 when x=-3 or x=4, so these numbers should be in your solution set.


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