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x² + x – 6 x2 – 3x – 4 Rational Inequality 1. Put the rational inequality in general form. R(x) > 0 Q(x) where > can be replaced by <,< and 2 2. Write the inequality into a single rational expression on the left side. (You can refer to the review section for solving unlike denominators) 3. Set the numerator and denominator equal to zero and solve. The values you get are called critical values. 4. Plot the critical values on a number line, breaking the number line into intervals. 5. Substitute critical values to the inequality to determine if the 6. 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. 7. Use interval notation or set notation to write the final answer. (-3,–1)U[2,4)

x² + x – 6 x2 – 3x – 4 Rational Inequality 1. Put the rational inequality in general form. R(x) > 0 Q(x) where > can be replaced by <,< and 2 2. Write the inequality into a single rational expression on the left side. (You can refer to the review section for solving unlike denominators) 3. Set the numerator and denominator equal to zero and solve. The values you get are called critical values. 4. Plot the critical values on a number line, breaking the number line into intervals. 5. Substitute critical values to the inequality to determine if the 6. 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. 7. Use interval notation or set notation to write the final answer. (-3,–1)U[2,4)

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.7: Solving Inequalities
Problem 2E: To solve the nonlinear inequality x+1x20 , we first observe that the number, ____ and ____ are zeros...
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x² + x – 6 Rational Inequality x2 – 3x – 4 | 1. Put the rational inequality in general form. R(x) Q(x) where > can be replaced by <,s and 2 2. Write the inequality into a single rational expression on the left side. (You can refer to the review section for solving unlike denominators) 3. Set the numerator and denominator equal to zero and solve. The values you get are called critical values. 4. Plot the critical values on a number line, breaking the number line into intervals. 5. Substitute critical values to the inequality to determine if the 6. 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. 7. Use interval notation or set notation to write the final answer. [-3,–1) U[ 2,4)
Transcribed Image Text:x² + x – 6 Rational Inequality x2 – 3x – 4 | 1. Put the rational inequality in general form. R(x) Q(x) where > can be replaced by <,s and 2 2. Write the inequality into a single rational expression on the left side. (You can refer to the review section for solving unlike denominators) 3. Set the numerator and denominator equal to zero and solve. The values you get are called critical values. 4. Plot the critical values on a number line, breaking the number line into intervals. 5. Substitute critical values to the inequality to determine if the 6. 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. 7. Use interval notation or set notation to write the final answer. [-3,–1) U[ 2,4)
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