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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 #101 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 23 x + 86 and y = 14 x + 57

Possible Answers:

${x=- \frac{29}{9}}$

${x=\frac{29}{9}}$

$\uptext{x}=6$

${x = - \frac{58}{9}}$

$\uptext{x}=-5$

Correct answer:

${x=- \frac{29}{9}}$

Explanation:

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

23 x + 86 = 14 x + 57

23 x + 86-86=14 x + 57-86

23 x=14 x - 29

23 x-14 x=14 x - 29-14 x

9 x=-29

$x=- \frac{29}{9}$

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Example Question #102 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 42 x - 46 and y = 2 x - 86

Possible Answers:

$\uptext{x}=-5$

{x = -2}

{x=1}

{x=-1}

$\uptext{x}=6$

Correct answer:

{x=-1}

Explanation:

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

42 x - 46 = 2 x - 86

42 x - 46+46=2 x - 86+46

42 x=2 x - 40

42 x-2 x=2 x - 40-2 x

40 x=-40

x=-1

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Example Question #103 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 7 x + 3 and y = 40 x - 90

Possible Answers:

$\uptext{x}=-5$

${x=\frac{31}{11}}$

$\uptext{x}=6$

${x=- \frac{31}{11}}$

${x = \frac{62}{11}}$

Correct answer:

${x=\frac{31}{11}}$

Explanation:

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

7 x + 3 = 40 x - 90

7 x + 3-3=40 x - 90-3

7 x=40 x - 93

7 x-40 x=40 x - 93-40 x

- 33 x=-93

$x=\frac{31}{11}$

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Example Question #101 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 7 x - 35 and y = 31 x + 71

Possible Answers:

$\uptext{x}=-5$

${x=\frac{53}{12}}$

${x=- \frac{53}{12}}$

${x = - \frac{53}{6}}$

$\uptext{x}=6$

Correct answer:

${x=- \frac{53}{12}}$

Explanation:

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

7 x - 35 = 31 x + 71

7 x - 35+35=31 x + 71+35

7 x=31 x + 106

7 x-31 x=31 x + 106-31 x

- 24 x=106

$x=- \frac{53}{12}$

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Example Question #102 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 17 x - 31 and y = 42 x + 33

Possible Answers:

${x=\frac{64}{25}}$

$\uptext{x}=6$

${x = - \frac{128}{25}}$

$\uptext{x}=-5$

${x=- \frac{64}{25}}$

Correct answer:

${x=- \frac{64}{25}}$

Explanation:

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

17 x - 31 = 42 x + 33

17 x - 31+31=42 x + 33+31

17 x=42 x + 64

17 x-42 x=42 x + 64-42 x

- 25 x=64

$x=- \frac{64}{25}$

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Example Question #563 : High School: Algebra

Where do the following lines intersect?

y = 44 x + 18 and y = 5 x + 34

Possible Answers:

${x=- \frac{16}{39}}$

$\uptext{x}=-5$

$\uptext{x}=6$

${x = \frac{32}{39}}$

${x=\frac{16}{39}}$

Correct answer:

${x=\frac{16}{39}}$

Explanation:

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

44 x + 18 = 5 x + 34

44 x + 18-18=5 x + 34-18

44 x=5 x + 16

44 x-5 x=5 x + 16-5 x

39 x=16

$x=\frac{16}{39}$

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Example Question #564 : High School: Algebra

Where do the following lines intersect?

y = 45 x - 35 and y = 15 x - 58

Possible Answers:

$\uptext{x}=6$

$\uptext{x}=-5$

${x = - \frac{23}{15}}$

${x=\frac{23}{30}}$

${x=- \frac{23}{30}}$

Correct answer:

${x=- \frac{23}{30}}$

Explanation:

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

45 x - 35 = 15 x - 58

45 x - 35+35=15 x - 58+35

45 x=15 x - 23

45 x-15 x=15 x - 23-15 x

30 x=-23

$x=- \frac{23}{30}$

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Example Question #565 : High School: Algebra

Where do the following lines intersect?

y = 4 x + 93 and y = 34 x - 68

Possible Answers:

$\uptext{x}=-5$

${x=- \frac{161}{30}}$

${x = \frac{161}{15}}$

$\uptext{x}=6$

${x=\frac{161}{30}}$

Correct answer:

${x=\frac{161}{30}}$

Explanation:

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

4 x + 93 = 34 x - 68

4 x + 93-93=34 x - 68-93

4 x=34 x - 161

4 x-34 x=34 x - 161-34 x

- 30 x=-161

$x=\frac{161}{30}$

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Example Question #566 : High School: Algebra

Where do the following lines intersect?

y = 49 x + 81 and y = 13 x + 75

Possible Answers:

${x=\frac{1}{6}}$

${x=- \frac{1}{6}}$

$\uptext{x}=-5$

$\uptext{x}=6$

${x = - \frac{1}{3}}$

Correct answer:

${x=- \frac{1}{6}}$

Explanation:

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

49 x + 81 = 13 x + 75

49 x + 81-81=13 x + 75-81

49 x=13 x - 6

49 x-13 x=13 x - 6-13 x

36 x=-6

$x=- \frac{1}{6}$

Report an Error

Example Question #104 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 16 x + 57 and y = 23 x - 24

Possible Answers:

$\uptext{x}=-5$

$\uptext{x}=6$

${x = \frac{162}{7}}$

${x=- \frac{81}{7}}$

${x=\frac{81}{7}}$

Correct answer:

${x=\frac{81}{7}}$

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 + 57 = 23 x - 24

16 x + 57-57=23 x - 24-57

16 x=23 x - 81

16 x-23 x=23 x - 81-23 x

- 7 x=-81

$x=\frac{81}{7}$

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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 #101 : Reasoning With Equations & Inequalities

Example Question #102 : Reasoning With Equations & Inequalities

Example Question #103 : Reasoning With Equations & Inequalities

Example Question #101 : Reasoning With Equations & Inequalities

Example Question #102 : Reasoning With Equations & Inequalities

Example Question #563 : High School: Algebra

Example Question #564 : High School: Algebra

Example Question #565 : High School: Algebra

Example Question #566 : High School: Algebra

Example Question #104 : Reasoning With Equations & Inequalities

All Common Core: High School - Algebra Resources

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