Solving Inequalities G9

Introduction:

Solving inequalities are very important when we want to find the values of x where the function is positive or negative .

Example 1: solve x squared – x – 6 is greater than 0.
Solution 1: (x-3)(x plus 2) is greater than 0. Check intervals: – infinity to -2, -2 to 3 and 3 to infinity. Ok x equals-3,, (-3)(-1) equals 6.Now x equals 0 yields -6 and x equals 4 equals (1)(6) equals 6. There. Therefore the function is positive on -infinity to -2 and 3 to infinity.

Example 2: where is the function f(x) equals x(x-2)(x-4) negative?
Solution 2: The intervals that need to be checked are – infinity to 0, 0 to 2, 2 to 4 and 4 to infinit-1 gives us —1( -5)(-3) equals -15. 1 gives us 1(-3)(-2) equals 6 . 3 gives us 3(-1)(1) equals -3. And 5 equals 5(1)(3) equals 15. Therefore the function is negative on the interval from – infinity to 0 and 2 to 4.

Conclusion:

Solving inequalities like these help us graph quadratic and cubic functions.