Rational-Inequality (1).pptx
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This document provides steps for solving rational equations and inequalities: 1. Find the least common denominator and clear fractions by multiplying both sides by the LCD. 2. For inequalities, write the expression as a single rational term and set the numerator and denominator equal to 0 to find critical values. 3. Plot critical values on a number line and test values in each interval to determine if it satisfies the original inequality.
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Rational-Inequality (1).pptx
- 1. Solving Rational Equations and Inequalities M11GM-Ib-3 solves rational equations and inequalities.
- 3. 1. Find the Least Common Denominator(LCD).
- 4. 2. Multiply both sides of the equation by its the LCD.
- 5. 3. Apply the Distributive Property and then simplify.
- 6. 4. Find all the possible values of x.
- 7. 5. Check each value by substituting into original equation and reject any extraneous root/s
- 12. Rational Inequality 2. Write the inequality into a single rational expression on the left side. (You can refer to the review section for solving unlike denominators)
- 13. Rational Inequality 4. Plot the critical values on a number line, breaking the number line into intervals. Numerator: + 1 = 0 = 1 Denominator: 2 = 0 = 2
- 14. Rational Inequality 5. Substitute critical values to the inequality to determine if the endpoints of the intervals in the solution should be included or not. Numerator: + 1 = 0 = 1 Denominator: 2 = 0 = 2
- 15. Rational Inequality 5. Select test values in each interval and substitute those values into the inequality. Note: If the test value makes the inequality true, then the entire interval is a solution to the inequality. If the test value makes the inequality false, then the entire interval is not a solution to the inequality.
- 16. Rational Inequality 6. Use interval notation or set notation to write the final answer.
- 17. Rational Inequality Step 1. Put the rational inequality in the general form where > can be replaced by <, . Step 2. Write the inequality into a single rational expression on the left-hand side. Step 3. Set the numerator and denominator equal to zero and solve. The values you get are called critical values. Step 4. Plot the critical values on a number line, breaking the number line into intervals. Step 5. Substitute critical values to the inequality to determine if the endpoints of the intervals in the solution should be included or not.
- 18. Rational Inequality Step 6. Select test values in each interval and substitute those values into the inequality. Note: a. If the test value makes the inequality TRUE, then the entire interval is a solution to the inequality b. If the test value makes the inequality FALSE, then the entire interval is not a solution to the inequality.
- 19. Rational Inequality Step 7. Use interval notation to write the final answer..