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Common Core: High School - Algebra : Reasoning with Equations & Inequalities

Study concepts, example questions & explanations for Common Core: High School - Algebra

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All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Where do the following lines intersect?

y = 41 x + 85 and y = 19 x + 84

Possible Answers:

$x = - \frac{1}{22}$

x = -5

x = 6

$x = \frac{1}{22}$

$x = - \frac{1}{11}$

Correct answer:

$x = - \frac{1}{22}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

41 x + 85 = 19 x + 84

41 x + 85 - 85 = 19 x + 84 - 85

41 x = 19 x - 1

41 x - 19 x = 19 x - 1 - 19 x

22 x = -1

$x = - \frac{1}{22}$

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Example Question #2 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Where do the following lines intersect?

y = 16 x + 86 and y = 2 x - 78

Possible Answers:

$x = - \frac{82}{7}$

$x = - \frac{164}{7}$

x = -5

$x = \frac{82}{7}$

x = 6

Correct answer:

$x = - \frac{82}{7}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

16 x + 86 = 2 x - 78

16 x + 86 - 86 = 2 x - 78 - 86

16 x = 2 x - 164

16 x - 2 x = 2 x - 164 - 2 x

14 x = -164

$x = - \frac{82}{7}$

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Example Question #1 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Where do the following lines intersect?

y = 6 x - 13 and y = 22 x + 43

Possible Answers:

$x = \frac{7}{2}$

x = -7

x = 6

$x = - \frac{7}{2}$

x = -5

Correct answer:

$x = - \frac{7}{2}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

6 x - 13 = 22 x + 43

6 x - 13 + 13 = 22 x + 43 + 13

6 x = 22 x + 56

6 x - 22 x = 22 x + 56 - 22 x

- 16 x = 56

$x = - \frac{7}{2}$

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Example Question #4 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Where do the following lines intersect?

y = 11 x + 72 and y = 27 x + 31

Possible Answers:

$- \frac{41}{16}$

$\frac{41}{8}$

$x = \frac{41}{16}$

x = -5

x = 6

Correct answer:

$x = \frac{41}{16}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

11 x + 72 = 27 x + 31

11 x + 72 - 72 = 27 x + 31 - 72

11 x = 27 x - 41

11 x - 27 x = 27 x - 41 - 27 x

- 16 x = -41

$x = \frac{41}{16}$

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Example Question #5 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Where do the following lines intersect?

y = 16 x - 39 and y = 29 x + 91

Possible Answers:

x = 10

x = -5

x = -20

x = -10

x = 6

Correct answer:

x = -10

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

16 x - 39 = 29 x + 91

16 x - 39 + 39 = 29 x + 91 + 39

16 x = 29 x + 130

16 x - 29 x = 29 x + 130 - 29 x

- 13 x = 130

x = -10

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Example Question #11 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Where do the following lines intersect?

y = 21 x - 47 and y = 40 x + 28

Possible Answers:

x = -5

$x = - \frac{150}{19}$

x = 6

$x = - \frac{75}{19}$

$x = \frac{75}{19}$

Correct answer:

$x = - \frac{75}{19}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x$ .

21 x - 47 = 40 x + 28

21 x - 47 + 47 = 40 x + 28 + 47

21 x = 40 x + 75

21 x - 40 x = 40 x + 75 - 40 x

- 19 x = 75

$x = - \frac{75}{19}$

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Example Question #12 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Where do the following lines intersect?

y = 28 x - 40 and y = 34 x - 90

Possible Answers:

${x=- \frac{25}{3}}$

$\uptext{x}=-5$

$\uptext{x}=6$

${x=\frac{25}{3}}$

${x = \frac{50}{3}}$

Correct answer:

${x=\frac{25}{3}}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

28 x - 40 = 34 x - 90

28 x - 40+40=34 x - 90+40

28 x=34 x - 50

28 x-34 x=34 x - 50-34 x

- 6 x=-50

$x=\frac{25}{3}$

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Example Question #81 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 14 x + 36 and y = 26 x - 10

Possible Answers:

${x=- \frac{23}{6}}$

${x=\frac{23}{6}}$

${x = \frac{23}{3}}$

$\uptext{x}=-5$

$\uptext{x}=6$

Correct answer:

${x=\frac{23}{6}}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

14 x + 36 = 26 x - 10

14 x + 36-36=26 x - 10-36

14 x=26 x - 46

14 x-26 x=26 x - 46-26 x

- 12 x=-46

$x=\frac{23}{6}$

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Example Question #14 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Where do the following lines intersect?

y = 48 x + 21 and y = 43 x + 15

Possible Answers:

$\uptext{x}=6$

${x=\frac{6}{5}}$

${x = - \frac{12}{5}}$

${x=- \frac{6}{5}}$

$\uptext{x}=-5$

Correct answer:

${x=- \frac{6}{5}}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

48 x + 21 = 43 x + 15

48 x + 21-21=43 x + 15-21

48 x=43 x - 6

48 x-43 x=43 x - 6-43 x

5 x=-6

$x=- \frac{6}{5}$

Report an Error

Example Question #82 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 48 x + 29 and y = 29 x - 87

Possible Answers:

$\uptext{x}=6$

${x = - \frac{232}{19}}$

${x=\frac{116}{19}}$

$\uptext{x}=-5$

${x=- \frac{116}{19}}$

Correct answer:

${x=- \frac{116}{19}}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

48 x + 29 = 29 x - 87

48 x + 29-29=29 x - 87-29

48 x=29 x - 116

48 x-29 x=29 x - 116-29 x

19 x=-116

$x=- \frac{116}{19}$

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All Common Core: High School - Algebra Resources

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Common Core: High School - Algebra : Reasoning with Equations & Inequalities

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #1 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Example Question #2 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Example Question #1 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Example Question #4 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Example Question #5 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Example Question #11 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Example Question #12 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Example Question #81 : Reasoning With Equations & Inequalities

Example Question #14 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Example Question #82 : Reasoning With Equations & Inequalities

All Common Core: High School - Algebra Resources

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