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Common Core: High School - Algebra : High School: Algebra

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

Where do the following lines intersect?

$\displaystyle y = 48 x + 35$ and $\displaystyle y = 23 x + 83$

Possible Answers:

${x=\frac{48}{25}}$ $\displaystyle {x=\frac{48}{25}}$

$\uptext{x}=6$ $\displaystyle \uptext{x}=6$

${x = \frac{96}{25}}$ $\displaystyle {x = \frac{96}{25}}$

${x=- \frac{48}{25}}$ $\displaystyle {x=- \frac{48}{25}}$

$\uptext{x}=-5$ $\displaystyle \uptext{x}=-5$

Correct answer:

${x=\frac{48}{25}}$ $\displaystyle {x=\frac{48}{25}}$

Explanation:

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

$\displaystyle 48 x + 35 = 23 x + 83$

$\displaystyle 48 x + 35-35=23 x + 83-35$

$\displaystyle 48 x=23 x + 48$

$\displaystyle 48 x-23 x=23 x + 48-23 x$

25 x=48 $\displaystyle 25 x=48$

$x=\frac{48}{25}$ $\displaystyle x=\frac{48}{25}$

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Example Question #91 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

$\displaystyle y = 23 x - 53$ and $\displaystyle y = 41 x + 35$

Possible Answers:

${x=\frac{44}{9}}$ $\displaystyle {x=\frac{44}{9}}$

$\uptext{x}=-5$ $\displaystyle \uptext{x}=-5$

${x=- \frac{44}{9}}$ $\displaystyle {x=- \frac{44}{9}}$

${x = - \frac{88}{9}}$ $\displaystyle {x = - \frac{88}{9}}$

$\uptext{x}=6$ $\displaystyle \uptext{x}=6$

Correct answer:

${x=- \frac{44}{9}}$ $\displaystyle {x=- \frac{44}{9}}$

Explanation:

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

$\displaystyle 23 x - 53 = 41 x + 35$

$\displaystyle 23 x - 53+53=41 x + 35+53$

$\displaystyle 23 x=41 x + 88$

$\displaystyle 23 x-41 x=41 x + 88-41 x$

$\displaystyle - 18 x=88$

$x=- \frac{44}{9}$ $\displaystyle x=- \frac{44}{9}$

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Example Question #91 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

$\displaystyle y = 20 x + 63$ and $\displaystyle y = 39 x + 74$

Possible Answers:

$\uptext{x}=6$ $\displaystyle \uptext{x}=6$

$\uptext{x}=-5$ $\displaystyle \uptext{x}=-5$

${x=\frac{11}{19}}$ $\displaystyle {x=\frac{11}{19}}$

${x = - \frac{22}{19}}$ $\displaystyle {x = - \frac{22}{19}}$

${x=- \frac{11}{19}}$ $\displaystyle {x=- \frac{11}{19}}$

Correct answer:

${x=- \frac{11}{19}}$ $\displaystyle {x=- \frac{11}{19}}$

Explanation:

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

$\displaystyle 20 x + 63 = 39 x + 74$

$\displaystyle 20 x + 63-63=39 x + 74-63$

$\displaystyle 20 x=39 x + 11$

$\displaystyle 20 x-39 x=39 x + 11-39 x$

$\displaystyle - 19 x=11$

$x=- \frac{11}{19}$ $\displaystyle x=- \frac{11}{19}$

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Example Question #92 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

$\displaystyle y = 14 x - 90$ and $\displaystyle y = 18 x + 62$

Possible Answers:

$\displaystyle {x = -76}$

{x=38} $\displaystyle {x=38}$

$\uptext{x}=-5$ $\displaystyle \uptext{x}=-5$

{x=-38} $\displaystyle {x=-38}$

$\uptext{x}=6$ $\displaystyle \uptext{x}=6$

Correct answer:

{x=-38} $\displaystyle {x=-38}$

Explanation:

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

$\displaystyle 14 x - 90 = 18 x + 62$

$\displaystyle 14 x - 90+90=18 x + 62+90$

$\displaystyle 14 x=18 x + 152$

$\displaystyle 14 x-18 x=18 x + 152-18 x$

$\displaystyle - 4 x=152$

x=-38 $\displaystyle x=-38$

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Example Question #93 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

$\displaystyle y = 2 x + 3$ and $\displaystyle y = 28 x - 64$

Possible Answers:

${x=\frac{67}{26}}$ $\displaystyle {x=\frac{67}{26}}$

$\uptext{x}=-5$ $\displaystyle \uptext{x}=-5$

$\uptext{x}=6$ $\displaystyle \uptext{x}=6$

${x=- \frac{67}{26}}$ $\displaystyle {x=- \frac{67}{26}}$

${x = \frac{67}{13}}$ $\displaystyle {x = \frac{67}{13}}$

Correct answer:

${x=\frac{67}{26}}$ $\displaystyle {x=\frac{67}{26}}$

Explanation:

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

$\displaystyle 2 x + 3 = 28 x - 64$

$\displaystyle 2 x + 3-3=28 x - 64-3$

$\displaystyle 2 x=28 x - 67$

$\displaystyle 2 x-28 x=28 x - 67-28 x$

$\displaystyle - 26 x=-67$

$x=\frac{67}{26}$ $\displaystyle x=\frac{67}{26}$

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Example Question #92 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

$\displaystyle y = 2 x + 62$ and $\displaystyle y = 19 x - 29$

Possible Answers:

$\uptext{x}=6$ $\displaystyle \uptext{x}=6$

${x=- \frac{91}{17}}$ $\displaystyle {x=- \frac{91}{17}}$

${x = \frac{182}{17}}$ $\displaystyle {x = \frac{182}{17}}$

${x=\frac{91}{17}}$ $\displaystyle {x=\frac{91}{17}}$

$\uptext{x}=-5$ $\displaystyle \uptext{x}=-5$

Correct answer:

${x=\frac{91}{17}}$ $\displaystyle {x=\frac{91}{17}}$

Explanation:

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

$\displaystyle 2 x + 62 = 19 x - 29$

$\displaystyle 2 x + 62-62=19 x - 29-62$

$\displaystyle 2 x=19 x - 91$

$\displaystyle 2 x-19 x=19 x - 91-19 x$

$\displaystyle - 17 x=-91$

$x=\frac{91}{17}$ $\displaystyle x=\frac{91}{17}$

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Example Question #555 : High School: Algebra

Where do the following lines intersect?

$\displaystyle y = 22 x - 37$ and $\displaystyle y = 48 x - 11$

Possible Answers:

{x=1} $\displaystyle {x=1}$

$\displaystyle {x = -2}$

$\uptext{x}=6$ $\displaystyle \uptext{x}=6$

$\uptext{x}=-5$ $\displaystyle \uptext{x}=-5$

{x=-1} $\displaystyle {x=-1}$

Correct answer:

{x=-1} $\displaystyle {x=-1}$

Explanation:

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

$\displaystyle 22 x - 37 = 48 x - 11$

$\displaystyle 22 x - 37+37=48 x - 11+37$

$\displaystyle 22 x=48 x + 26$

$\displaystyle 22 x-48 x=48 x + 26-48 x$

$\displaystyle - 26 x=26$

x=-1 $\displaystyle x=-1$

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Example Question #101 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

$\displaystyle y = 23 x + 86$ and $\displaystyle y = 14 x + 57$

Possible Answers:

$\uptext{x}=6$ $\displaystyle \uptext{x}=6$

$\uptext{x}=-5$ $\displaystyle \uptext{x}=-5$

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

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

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

Correct answer:

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

Explanation:

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

$\displaystyle 23 x + 86 = 14 x + 57$

$\displaystyle 23 x + 86-86=14 x + 57-86$

$\displaystyle 23 x=14 x - 29$

$\displaystyle 23 x-14 x=14 x - 29-14 x$

9 x=-29 $\displaystyle 9 x=-29$

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

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Example Question #102 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

$\displaystyle y = 42 x - 46$ and $\displaystyle y = 2 x - 86$

Possible Answers:

{x=-1} $\displaystyle {x=-1}$

$\displaystyle {x = -2}$

$\uptext{x}=6$ $\displaystyle \uptext{x}=6$

{x=1} $\displaystyle {x=1}$

$\uptext{x}=-5$ $\displaystyle \uptext{x}=-5$

Correct answer:

{x=-1} $\displaystyle {x=-1}$

Explanation:

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

$\displaystyle 42 x - 46 = 2 x - 86$

$\displaystyle 42 x - 46+46=2 x - 86+46$

$\displaystyle 42 x=2 x - 40$

$\displaystyle 42 x-2 x=2 x - 40-2 x$

$\displaystyle 40 x=-40$

x=-1 $\displaystyle x=-1$

Report an Error

Example Question #103 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

$\displaystyle y = 7 x + 3$ and $\displaystyle y = 40 x - 90$

Possible Answers:

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

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

$\uptext{x}=-5$ $\displaystyle \uptext{x}=-5$

$\uptext{x}=6$ $\displaystyle \uptext{x}=6$

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

Correct answer:

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

Explanation:

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

$\displaystyle 7 x + 3 = 40 x - 90$

$\displaystyle 7 x + 3-3=40 x - 90-3$

$\displaystyle 7 x=40 x - 93$

$\displaystyle 7 x-40 x=40 x - 93-40 x$

$\displaystyle - 33 x=-93$

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

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All Common Core: High School - Algebra Resources

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Common Core: High School - Algebra : High School: Algebra

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

All Common Core: High School - Algebra Resources

Example Questions

Example Question #15 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Example Question #91 : Reasoning With Equations & Inequalities

Example Question #91 : Reasoning With Equations & Inequalities

Example Question #92 : Reasoning With Equations & Inequalities

Example Question #93 : Reasoning With Equations & Inequalities

Example Question #92 : Reasoning With Equations & Inequalities

Example Question #555 : High School: Algebra

Example Question #101 : Reasoning With Equations & Inequalities

Example Question #102 : Reasoning With Equations & Inequalities

Example Question #103 : Reasoning With Equations & Inequalities

All Common Core: High School - Algebra Resources

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