CPM Homework Help : INT3 Problem 3-75

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3-75.

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

$| 2 x + 3 | < 5$
Step 1(a):
Solve the corresponding equations to determine the boundary points.
$2x+3=5$
$2x+3=−5$
Step 2(a):
Solving yields $x=−4$ 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):

$| 2 x + 3 | \geq 5$
Hint (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.
$|2(0)+3|\ge5→3\ge5$

$| 2 x - 3 | < 5$
Hint (c):
See the steps in part (a).

$| 2 x - 3 | \geq 5$
Answer (d):

$| 3 - 2 x | < 5$

$| 3 - 2 x | \geq 5$

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?

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