In Exercises 11–24, solve the equation. Graph the solution(s), if possible. 15. |m + 3| = 7

m + 3 = 7 or m + 3 = -7; m = 4 or m = -10

m + 3 = 7 or m + 3 = 7; m = 4 or m = 4

m + 3 = -7 or m + 3 = -7; m = -10 or m = -10

m + 3 = 0 or m + 3 = 7; m = -3 or m = 4

In Exercises 11–24, solve the equation. Graph the solution(s), if possible. 16. |q − 8| = 14

q - 8 = 14 or q - 8 = -14; q = 22 or q = -6

q - 8 = 14 or q - 8 = 14; q = 22 or q = 22

q - 8 = -14 or q - 8 = -14; q = -6 or q = -6

q - 8 = 8 or q - 8 = -8; q = 16 or q = 0

In Exercises 11–24, solve the equation. Graph the solution(s), if possible. 17. |−3d| = 15

-3d = 15 or -3d = -15; d = -5 or d = 5

-3d = 0 or -3d = 15; d = 0 or d = -5

-3d = 5 or -3d = -5; d = -5/3 or d = 5/3

-3d = 15 or -3d = 5; d = -5 or d = -5/3

In Exercises 11–24, solve the equation. Graph the solution(s), if possible. 18. |l/2| = 6

l/2 = 6 or l/2 = -6; l = 12 or l = -12

l/2 = 3 or l/2 = -3; l = 6 or l = -6

l/2 = 12 or l/2 = -12; l = 24 or l = -24

l/2 = 0 or l/2 = 6; l = 0 or l = 12

In Exercises 11–24, solve the equation. Graph the solution(s), if possible. 19. |4b − 5| = 19

4b - 5 = 19 or 4b - 5 = -19; b = 6 or b = -3.5

4b - 5 = 19 or 4b - 5 = -19; b = 3.5 or b = -6

4b - 5 = 19 or 4b - 5 = 19; b = 6 or b = 3.5

4b - 5 = 19 or 4b - 5 = -19; b = 0 or b = 6

In Exercises 11–24, solve the equation. Graph the solution(s), if possible. 22. −3|1 − 2/3 y| = −9

|1 - 2/3 y| = 3; 1 - 2/3 y = 3 or 1 - 2/3 y = -3; y = -3 or y = 6

|1 - 2/3 y| = -3; 1 - 2/3 y = -3 or 1 - 2/3 y = 3; y = 3 or y = -6

|1 - 2/3 y| = 9; 1 - 2/3 y = 9 or 1 - 2/3 y = -9; y = -12 or y = 15

|1 - 2/3 y| = 0; 1 - 2/3 y = 0; y = 1.5

In Exercises 11–24, solve the equation. Graph the solution(s), if possible. 24. 9|4p + 2| + 8 = 35

|4p + 2| = 3; 4p + 2 = 3 or 4p + 2 = -3; p = 0.25 or p = -1.25

|4p + 2| = 5; 4p + 2 = 5 or 4p + 2 = -5; p = 0.75 or p = -1.75

|4p + 2| = 1; 4p + 2 = 1 or 4p + 2 = -1; p = -0.25 or p = -0.75

|4p + 2| = 4; 4p + 2 = 4 or 4p + 2 = -4; p = 0.5 or p = -1.5

Which of the following correctly represents the minimum and maximum distances from Earth to the Sun on a number line?

91.4 million miles and 94.5 million miles

90.0 million miles and 95.0 million miles

92.0 million miles and 93.0 million miles

91.0 million miles and 95.5 million miles

WRITING EQUATIONS: The shoulder heights of the shortest and tallest miniature poodles are shown. Which of the following best represents these two heights on a number line?

The two heights are marked as points on the number line.

The two heights are shown as a single point on the number line.

The two heights are not shown on the number line.

The two heights are represented as a shaded region on the number line.

Your friend claims to know the correct answer. Is your friend correct?

There is not enough information to decide.

You randomly survey students about year-round school. The results are shown in the graph. a. Write and solve an absolute value equation to find the least and greatest percents of students who could be in favor of year-round school.

|x - 32| = 5, so x = 27% or x = 37%

|x - 32| = 10, so x = 22% or x = 42%

|x - 37| = 5, so x = 32% or x = 42%

|x - 27| = 5, so x = 22% or x = 32%

Does the claim that 1/3 of the student body is in favor of year-round school conflict with the survey data?

Yes, it conflicts with the survey data.

No, it matches the survey data.

The survey data is inconclusive.

The survey did not ask about year-round school.

The recommended weight of a soccer ball is 430 grams. The actual weight is allowed to vary by up to 20 grams. a. Write and solve an absolute value equation to find the minimum and maximum acceptable soccer ball weights.

|x - 430| = 20, so x = 410 grams or x = 450 grams

|x + 430| = 20, so x = 410 grams or x = 450 grams

|x - 430| = 20, so x = 420 grams or x = 440 grams

|x - 430| = 10, so x = 420 grams or x = 440 grams

Big Ideas 1.4 Exercises - Solving Linear Equations Quiz

72 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

An extraneous solution is:

a solution that does not satisfy the original equation

a solution that satisfies all equations

a solution that is always correct

a solution that is always positive

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Without calculating, how do you know that the equation |4x - 7| = -1 has no solution?

Because the absolute value of any expression cannot be negative.

Because 4x - 7 is always positive.

Because -1 is not a valid solution for x.

Because the equation has infinite solutions.

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In Exercises 3–10, simplify the expression. 3. |−9|

9

-9

0

1

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In Exercises 3–10, simplify the expression. 4. |−15|

15

-15

0

1

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In Exercises 3–10, simplify the expression. 5. |14| − |−14|

0

28

-28

14

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In Exercises 3–10, simplify the expression. 6. |−3| + |3|

6

0

3

-6

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In Exercises 3–10, simplify the expression. 7. −|−5 • (−7)|

-35

35

-70

0

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Big Ideas 1.4 Exercises - Solving Linear Equations

An extraneous solution is:

Without calculating, how do you know that the equation |4x - 7| = -1 has no solution?

In Exercises 3–10, simplify the expression. 3. |−9|

In Exercises 3–10, simplify the expression. 4. |−15|

In Exercises 3–10, simplify the expression. 5. |14| − |−14|

In Exercises 3–10, simplify the expression. 6. |−3| + |3|

In Exercises 3–10, simplify the expression. 7. −|−5 • (−7)|

In Exercises 3–10, simplify the expression. 8. |−0.8 • 10|

In Exercises 3–10, simplify the expression. 9. |27 ÷ −3|

In Exercises 3–10, simplify the expression. 10. |−12 ÷ 4|

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