1 / 7

8.5 Solving Rational Equations and Inequalities

Objective. Solve rational equations and inequalities. Vocabulary. rational equation extraneous solution rational inequality a. 8.5 Solving Rational Equations and Inequalities. x. =. 2. 3 x + 4. 2 x – 5. 11. 5 x. x – 2. x – 8. x – 2. x – 8.

tex
Download Presentation

8.5 Solving Rational Equations and Inequalities

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Objective Solve rational equations and inequalities. Vocabulary rational equation extraneous solution rational inequality a 8.5 Solving Rational Equations and Inequalities

  2. x = 2 3x + 4 2x – 5 11 5x x – 2 x – 8 x – 2 x – 8 Always check for extraneous solutions by substituting into the equation. Example 2A: Extraneous Solutions Solve each equation. + = Check:

  3. = + 2. 10 4 18 3 x x To eliminate the denominators, multiply each term of the equation by the least common denominator (LCD) of all of the expressions in the equation. Example 1: Solving Rational Equations x– = 3.

  4. Solve ≤ 3 by using a graph and a table. Use a graph. On a graphing calculator, Y1 = and Y2 = 3. x x–6 x x–6 Example 5: Using Graphs and Tables to Solve Rational Inequalities (9, 3) Which x-values gives us output y-values that are less 3? Vertical asymptote: x = 6

  5. Example 5 Continued Use a table. The table shows that Y1 is undefined when x = 6 and that Y1 ≤ Y2 when x ≥ 9. The solution of the inequality is x < 6 or x ≥ 9.

  6. Solve ≤ 3 6 x–8 To solve rational inequalities algebraically multiply each term by the LCD of all the denominators. You must consider two cases: the LCD is positive or the LCD is negative. Example 6: Solving Rational Inequalities Algebraically Case 1 LCD is positive. Step 1 Solve for x. Step 2 Consider the sign of the LCD. For Case 1, the solution must satisfy x ≥ 10 and x > 8, which simplifies to x ≥ 10.

  7. Solve ≤ 3 6 x–8 6 x–8 The solution set of the original inequality is the union of the solutions to both Case 1 and Case 2. The solution to the inequality ≤ 3 is x < 8 or x ≥ 10, or {x|x < 8  x ≥ 10}. Example 6 Con’t Case 2 LCD is negative. Step 2 Consider the sign of the LCD. Step 1 Solve for x. For Case 2, the solution must satisfy x ≤ 10 and x < 8, which simplifies to x < 8.

More Related