Section 2.4 Linear Inequalities and Applications 95 Student Check 3 Write an inequality that models each situation. Solve the inequality and answer the problem in a complete sentence. a. Bryan has math test scores of 68, 83, and 75. What score does he need to make on his fourth math test to have a test average of at least 70? b. Tomekia’s final grade in her math class is based on a weighted average. The weights are as follows: homework (5%), quizzes (20%), tests (45%), and final exam (30%). If Tomekia’s homework average is 100, quiz average is 84, and test average is 80, what does she need on her final exam to have at least an 80 average in the class? c. Jared and Angela are planning their wedding reception. A reception hall charges $1500 plus $20 per person. How many people can they invite to their reception to have a cost of at most $4000? Troubleshooting Common Errors Some common errors associated with linear inequalities are shown. Objective 4 Examples A problem and an incorrect solution are given. Provide the correct solution and an explanation of the error. 4a. Write the set 5xux<-56 in interval notation. Incorrect Solution Correct Solution and Explanation The interval notation is (- 5, -∞). We always begin the interval with the smallest number and end the interval with the largest number in the set. Therefore, it should be (-∞, -5). 4b. Draw the graph that represents the set given by 5xux<-56. Incorrect Solution Correct Solution and Explanation The graph is: The number -5 is not included in the solution set. So, we should have a parenthesis on -5. –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 4c. Solve the inequality 5 - 3x ≤ -4. Incorrect Solution Correct Solution and Explanation 5 - 3x≤-4 When each side of an inequality is divided by a negative number, we must reverse the inequality symbol. 5 - 3x≤-4 5 - 3x - 5≤-4 - 5 -3x≤-9 x ≥ 3 So, the solution set is 3, ∞). 5 - 3x - 5≤-4 - 5 -3x≤-9 x ≤ 3 So, the solution set is (-∞, 3. Objective 4 ▶ Troubleshoot common errors. tation is 5 ≤ olut
hendricks_intermediate_algebra_1e_ch1_3
To see the actual publication please follow the link above