Section 2.7 Linear Inequalities in One Variable 173 4h. This is a compound inequality. We must isolate the variable in the middle. 3 < 2x + 1 < 7 -3 - 1 < 2x + 1 - 1 < 7 - 1 -4 < 2x < 6 -4 2 < 2x 2 < 6 2 Subtract 1 from each part. Simplify. Divide each part by 2. Simplify. -2 < x < 3 Since -2 < x < 3 is equivalent to x > -2 and x < 3, the graph consists of all the points greater than -2, but not including -2, and less than 3, but not including 3. This is equivalent to all points between, but not including, -2 and 3. –5 –4 –3 –2 –1 0 1 2 3 4 5 Interval notation: (-2, 3) Set-builder notation: Exu-2 < x < 3F Student Check 4 Solve each inequality. Graph the solution set and write the solution set in interval and set-builder notation. a. y + 3 < -2 b. -x ≤ 2 c. 7y - 1 > 6 d. 3(a + 2) - 7 ≥ -4a + 10 e. 1 3 y - 2ay + 1 2 b > 2 3 y + 1 6 f. 4(x - 3) + 1 ≥ 5(x + 2) - x g. 7x - 2(4x + 3) < 3(x + 5) - 4x h. 7 ≤ 6x - 3 ≤ 15 Applications There are a few key phrases that we need before we can solve applications relating to inequalities. Phrase 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 ≥ b a is at least b These phrases together with the ones presented in Chapter 1 enable us to write an inequality to solve application problems. ���������������������� Solving Applications of Linear 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 were listed in the chart above. 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 5 ▶ Solve applications of linear inequalities.
hendricks_beginning_algebra_1e_ch1_3
To see the actual publication please follow the link above