Page 95

hendricks_intermediate_algebra_1e_ch1_3

Section 2.4 Linear Inequalities and Applications 93 Verbal Statement Mathematical Statement a is less than b. a < b a is less than or equal to b. a is no more than b. a ≤ b a is at most b. a is greater than b. a > b a is greater than or equal to b. a is no less than b. a is at least b. a ≥ b Procedure: Solving Word Problems with Inequalities Step 1: Read the problem and determine the unknown. Assign a variable to the unknown value. Step 2: Read the problem and determine the given information. Step 3: Find the statement in the problem that states the inequality relationship, looking for key phrases that are listed in the preceding chart. Step 4: Use the statement in step 3 to write the inequality. Step 5: Apply the addition and multiplication properties of inequalities to solve the inequality. Step 6: Answer the question with a complete sentence. Objective 3 Examples Write an inequality that models each situation. Solve the inequality and answer the problem in a complete sentence. 3a. Sonia has math test scores of 73, 85, and 80. What score does she need to make on her fourth math test to have a test average of at least 80? Solution 3a. What is unknown? The score on the fourth test is unknown. Let x represent the fourth test score. What is given? The first three scores, 73, 85, and 80, are given. To obtain the inequality, we use the following statement. Average of the four tests is at least 80. 73 + 85 + 80 + x 4 ≥ 80 238 + x 4 Recall average is the sum of all items the number of items ≥ 80 Simplify the numerator of the fraction. 4a238 + x 4 b ≥ 4(80) Multiply each side by 4. 238 + x ≥ 320 Simplify. 238 + x - 238 ≥ 320 - 238 Subtract 238 from each side. x ≥ 82 Simplify. Sonia needs to make 82 or higher on her fourth test to have at least an 80 test average. We can check by substituting a number greater than or equal to 82 into the original inequality to see that the average is greater than or equal to 80. .


hendricks_intermediate_algebra_1e_ch1_3
To see the actual publication please follow the link above