### Home > CCA2 > Chapter 4 > Lesson 4.2.1 > Problem4-66

4-66.

Solve the following inequalities and draw a number line graph to represent each solution. Homework Help ✎

 a. $| 2 x + 3 |$ < 5Step 1(a):Solve the corresponding equations to determine the boundary points.$2x+3=5\\2x+3=−5$Step 2(a):Solving yields $x=−4\text{ or}\ x=1$.Plot these points on a number line.Step 3(a):Test a point in each region on the number line in the original inequality. Highlight the region(s) where the test point makes the inequality true.Answer (a): b. $| 2 x + 3 |$ ≥ 5Hint (b):See the steps in part (a).More Help (b):The boundary points in part (b) are the same as the ones in part (a). When you test a value between the boundary points you get a false statement.$|2(0)+3|\ge5→3\ge5$ c. $| 2 x - 3 |$ < 5Hint (c):See the steps in part (a). d. $| 2 x - 3 |$ ≥ 5Answer (d): e. $| 3 - 2 x |$ < 5 f. $| 3 - 2 x |$ ≥ 5 g. Describe any relationships you see among these six problems.Hint (g):How are the graphs of the 'less than' inequalities related to the graphs of the 'greater than or equal to' inequalities?