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2.7 Nonlinear Inequalities

2.7 Nonlinear Inequalities. Ex. 1 Solving a Quadratic Inequality. x 2 < x + 6. x 2 – x – 6 < 0. Now factor. 3 and –2 are called critical numbers . Put them on a number line and test each interval to see if it works. (x – 3)(x + 2) < 0. 3 -2. Pick a number

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2.7 Nonlinear Inequalities

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  1. 2.7 Nonlinear Inequalities

  2. Ex. 1 Solving a Quadratic Inequality x2 < x + 6 x2 – x – 6 < 0 Now factor. 3 and –2 are called critical numbers. Put them on a number line and test each interval to see if it works. (x – 3)(x + 2) < 0 3 -2 Pick a number bigger than 3. Does it work? ( ) -2 3 No. Now pick a number between –2 and 3. Does it work? Yes. Now a number < -2. Does it work? Ans. (-2,3)

  3. Ex. 2 Solving a polynomial inequality Take everything to the same side and factor. 2x3 + 5x2 > 12x 2x3 + 5x2 – 12x > 0 x(2x – 3)(x + 4) > 0 C.N.’s 0, 3/2, -4 () ( -4 0 3/2

  4. Ex. 3 Take the 3 over and get common denominators. What are the C.N.’s? Now put 5 and 8 on a number line and test the intervals. ) [ 5 8

  5. Ex. 4 An inequality involving fractions Take everything to one side. Now get common den. The num. gives imag. roots. Therefore, only C.N.’s are 2 and –3.

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