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messersmith_power_intermediate_algebra_1e_ch4_7_10

Step 5: The solution set of 5 x 3 0 contains the numbers in the interval where 5 x 3 is positive. This interval is (3, q). Negative Positive 3 5 x 3 Step 6: Since the inequality symbol is , the endpoint of the interval, 3, is not included in the solution set. The graph of the solution set is 5 2 1 1 2 5 The solution set is (3, q). YOU TRY 5 Solve 2 y 6 0. Graph the solution set, and write the solution in interval notation. EXAMPLE 6 Solve 7 a 2 3. Graph the solution set, and write the solution in interval notation. Solution Step 1: Get a zero on one side of the inequality symbol and only one rational expression on the other side. 7 a 2 3 7 a 2 3 0 Subtract 3. 7 a 2 3(a 2) a 2 0 Get a common denominator. 7 a 2 3a 6 a 2 0 Distribute. 1 3a a 2 0 Combine numerators, and combine like terms. From this point forward, we will work with the inequality 1 3a a 2 0. It is equivalent to the original inequality. Because the inequality symbol is , the solution set contains the interval(s) where 1 3a a 2 is negative. Step 2: Find the numbers that make the numerator equal 0 and any numbers that make the denominator equal 0. Step 3: Put 1 3 Numerator Denominator 1 3a 0 a 2 0 3a 1 a 2 a 1 3 and 2 on a number line to break it up into intervals. 2 13 1 3a a 2 www.mhhe.com/messersmith SECTION 10.7 Quadratic and Rational Inequalities 687


messersmith_power_intermediate_algebra_1e_ch4_7_10
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