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Rational Inequalities

Circle for this CV depends upon the inequality!. #2:. Circle for this CV is always open. OR. Now we test each interval to determine where to shade! Just pick a number in the interval and test it in the original equation. Find critical values by setting num and denom = 0. Page 5. Steps:

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Rational Inequalities

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  1. Circle for this CV depends upon the inequality! #2: Circle for this CV is always open OR Now we test each interval to determine where to shade! Just pick a number in the interval and test it in the original equation. Find critical values by setting num and denom = 0 Page 5 • Steps: • Get 0 on one side of inequality. • Get a common denominator and combine terms • Find Critical Values for numerator and denominator • Graph solutions on number line • Test each interval on number line CV for Numerator Rational Inequalities CV for Denominator Plot CV on number line -6: 3.17>3 - TRUE -1: -1>3 - FALSE 1: 9>3 - TRUE

  2. #3: -2: 11 2 - FALSE 0: -5 2 - TRUE 8:2.1 2 - FALSE Now we test each interval to determine where to shade! Just pick a number in the interval and test it in the original equation. Find critical values by setting num and denom = 0 Page 5 CV for Numerator CV for Denominator Plot CV on number line

  3. #6: Circles for these CV’s depends upon the inequality! Circles for these CV’s are always open Now we test each interval to determine where to shade! Just pick a number in the interval and test it in the original equation. -5: 2.3 0 - FALSE -3: -.7 0 - TRUE 0: .25 0 - FALSE 3: -.7 0 - TRUE 5: 2.3 0 - FALSE OR Page 5 Plot CV on number line CV for Numerator CV for Denominator

  4. #1: Page 5 Plot CV on number line CV for Numerator -1: .5 < 0 - FALSE 1: -1 < 0 - TRUE Open circle because of inequality 4: 8 < 0 - FALSE CV for Denominator Always open circle b/c it’s CV for denom

  5. #4: OR Page 5 Plot CV on number line CV for Numerator -4: 5 > 2 - TRUE Open circle because of inequality -2: 1 > 2 - FALSE CV for Denominator 0: 2.3 > 2 - TRUE Always open circle b/c it’s CV for denom

  6. #5: -5: -.8 0 - TRUE 0: .13 0 - FALSE 3: -.1 0 - TRUE 5: .33 0 - FALSE OR Page 5 Plot CV on number line CV for Numerator Closed circle because of inequality CV for Denominator Always open circle b/c it’s CV for denom

  7. Homework • Page 6 #2,6,10

  8. #2: Page 6 CV for Numerator Plot CV on number line Open circle because of inequality -8: 2.5 > 3 - FALSE CV for Denominator -5: 7 > 3 - TRUE 0: -.5 > 3 - FALSE Always open circle b/c it’s CV for denom

  9. #6: OR Page 6 CV for Numerator Plot CV on number line Open circle because of inequality -8: 4.3 < 7 - TRUE CV for Denominator -6: 15 < 7 - FALSE 0: -4.2 < 7 - TRUE Always open circle b/c it’s CV for denom

  10. #10: OR -5: 13 1 - TRUE 0: .5 1 - FALSE 2: 1.3 1 - TRUE Page 6 CV for Numerator Plot CV on number line Closed circle because of inequality CV for Denominator Always open circle b/c it’s CV for denom

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