1-6 Solving Compound and Absolute Value Inequalities
Solve each inequality. Graph the solution set on a number line.
13. SOLUTION: The solution of the inequality is
.
To graph, draw a solid circle at –1 and a solid circle at 0.5 and draw a line to connect the circles.
15. or
SOLUTION: The solution of the inequality is
.
To graph, draw an open circle at –4 and an arrow extending to the left and an open circle at 7 and an arrow
extending to the right.
17. SOLUTION: or
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The solution of the inequality is
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To graph, draw an open circle at –4 and an arrow extending to the left and an open circle at 7 and an arrow
extending to the right.
1-6 Solving Compound and Absolute Value Inequalities
17. SOLUTION: or
The solution of the inequality is
.
To graph, draw an open circle at –4 and an arrow extending to the left and an open circle at 4 and an arrow
extending to the right.
19. SOLUTION: The solution of the inequality is
.
To graph, draw a solid circle at
and a solid circle at
and draw a line to connect the circles.
21. SOLUTION: eSolutions Manual - Powered by Cognero
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To graph, draw a solid circle at
and a solid circle at
and draw a line to connect the circles.
1-6 Solving Compound and Absolute Value Inequalities
21. SOLUTION: or
The solution of the inequality is
.
To graph, draw a solid circle at
extending to the right.
and an arrow extending to the left and a solid circle at
and an arrow
Write an absolute value inequality for each graph.
23. SOLUTION: Write a compound inequality from the graph. Then determine what can be added or subtracted from each term so
that it is in the form -a < x + c < a. This implies that | x + c | < a.
This implies:
25. SOLUTION: Write a compound inequality from the graph. Then determine what can be added or subtracted from each term so
that it is in the form -a < x + c < a. This implies that | x + c | < a.
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This implies:
1-6 Solving
Compound and Absolute Value Inequalities
25. SOLUTION: Write a compound inequality from the graph. Then determine what can be added or subtracted from each term so
that it is in the form -a < x + c < a. This implies that | x + c | < a.
This implies:
27. SOLUTION: Write a compound inequality from the graph. Then determine what can be added or subtracted from each term so
that it is in the form x < -a or x > a. This implies that | x + c | > a.
or
This implies:
29. SOLUTION: Write a compound inequality from the graph. Then determine what can be added or subtracted from each term so
that it is in the form x < –a or x > a. This implies that | x + c | > a.
or
This implies:
31. DOGS The Labrador retriever is one of the most recognized and popular dogs kept as a pet. Using the information
given, write a compound inequality to describe the range of healthy weights for a fully grown female Labrador
retriever.
SOLUTION: Let w represent the weight of a female Labrador.
The weight of a fully grown female Labrador ranges from 55 units to 77 units.
So:
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or
This implies:
1-6 Solving
Compound and Absolute Value Inequalities
31. DOGS The Labrador retriever is one of the most recognized and popular dogs kept as a pet. Using the information
given, write a compound inequality to describe the range of healthy weights for a fully grown female Labrador
retriever.
SOLUTION: Let w represent the weight of a female Labrador.
The weight of a fully grown female Labrador ranges from 55 units to 77 units.
So:
Solve each inequality. Graph the solution set on a number line.
33. SOLUTION: The solution set is:
To graph, draw an open circle at 2 and an open circle at 4 and draw a line to connect the circles.
35. SOLUTION: or
The solution set is:
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To graph,
an open
circle
extending to the right.
at –15 and an arrow extending to the left and an open circle at 15 and an arrow
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To graph, draw an open circle at 2 and an open circle at 4 and draw a line to connect the circles.
1-6 Solving Compound and Absolute Value Inequalities
35. SOLUTION: or
The solution set is:
To graph, draw an open circle at –15 and an arrow extending to the left and an open circle at 15 and an arrow
extending to the right.
37. SOLUTION: The solution set is:
To graph, draw an open circle at –1 and an arrow extending to the left and an open circle at 5 and an arrow
extending to the right.
39. SOLUTION: or
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extending to the right.
1-6 Solving Compound and Absolute Value Inequalities
39. SOLUTION: or
The solution set is:
To graph, draw an open circle at
extending to the right.
and an arrow extending to the left and an open circle at
and an arrow
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