GENERAL MATHEMATICS THE SOLVING OF RATIONAL INEQUALITY
- 2. A rational inequality is an inequality involving rational expressions which can be solved for all unknown values satisfying the inequality. 𝟓 � � ≤ 𝟐 � � 𝑥 − 𝟑 𝟑 𝑥
- 4. Procedure for Solving Rational Inequalities To solve rational inequalities: (a) Rewrite the inequality as a single fraction on one side of the inequality symbol and 0 on the other side.
- 5. Procedure for Solving Rational Inequalities To solve rational inequalities: (b) Determine over what intervals the fraction takes on positive and negative values.
- 6. Procedure for Solving Rational Inequalities To solve rational inequalities: (b) Determine over what intervals the fraction takes on positive and negative values. i. locate the x-values for which the rational expression is zero or undefined (factoring the numerator and denominator is a useful strategy).
- 7. Procedure for Solving Rational Inequalities To solve rational inequalities: (b) Determine over what intervals the fraction takes on positive and negative values. ii. Mark the numbers found in (i) on a number line. Use a shaded circle to indicate that the value is included in the solution set, and a hollow circle to indicate that the value is excluded. These numbers partition the number line into intervals.
- 8. Procedure for Solving Rational Inequalities To solve rational inequalities: (b) Determine over what intervals the fraction takes on positive and negative values. iii. Select a test point within the interior of each interval in (ii). The sign of the rational expression at this test point is also the sign of the rational expression at each interior point in the aforementioned interval.
- 9. Procedure for Solving Rational Inequalities To solve rational inequalities: (b) Determine over what intervals the fraction takes on positive and negative values. iv. Summarize the intervals containing the solutions.
- 11. An INEQUALITY may have infinitely many solutions. The set of all solutions can be expressed using set notation and interval notation.
- 15. Step 1. Write the inequality in general form. Step 2. Determine the critical points/values. Step 3. Use the critical points to separate the number line into intervals. Step 4. Test for critical points. Step 5. Express the answer in interval notation. Solving Rational Inequalities Example 2𝑥 ≥ 1 𝑥 + 1
- 16. Solving Rational Inequalities 2 𝑥 𝑥 + 1 ≥ 1
- 18. to Step 4. Test for critical points. Step 5. Express the answer in interval notation. Solving Rational Inequalities Example Step 1. Write the inequality in general form. 3 1 < 𝑥 − 2 Step 2. Determine the critical points/values. Step 3. Use the critical points separate the number line into intervals.
- 19. Solving Rational Inequalities < 3 1 𝑥 − 2 𝑥 Exampl e
- 20. Solving Rational Inequalities 3 1 𝑥 − 2 < 𝑥 Exampl e
- 21. Solving Rational Inequalities Example 3 1 𝑥 − 2 < 𝑥
Editor's Notes
- #12: Presenter 2024-08-21 18:45:00 -------------------------------------------- A OPEN, B OPEN THE SET OF ALL X SUCH THAT X IS GREATER THAN A BUT LESS THAN B
- #13: Presenter 2024-08-21 18:45:00 -------------------------------------------- A OPEN, B OPEN THE SET OF ALL X SUCH THAT X IS GREATER THAN A BUT LESS THAN B
- #14: Presenter 2024-08-21 18:45:00 -------------------------------------------- A OPEN, B OPEN THE SET OF ALL X SUCH THAT X IS GREATER THAN A BUT LESS THAN B