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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

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Example Questions

Example Question #171 : Reasoning With Equations & Inequalities

Where do the following equations intersect?

y = 3 x - 20

y = 42

Possible Answers:

$\left( \frac{23}{42} , 42 \right)$

$\left( \frac{62}{3} , 42 \right)$

$\left( \frac{23}{42} , 25 \right)$

$\left( \infty , 42 \right)$

$\left( \frac{23}{42} , \frac{2}{3} \right)$

Correct answer:

$\left( \frac{62}{3} , 42 \right)$

Explanation:

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

3 x - 20 = 42

Now we add to each side.

3 x = 62

Now we divide by on each side.

$x = \frac{62}{3}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = 3 \cdot \frac{62}{3} -20$

y = 62 -20

y = 42

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Example Question #172 : Reasoning With Equations & Inequalities

Where do the following equations intersect?

y = 42 x - 2

y = - 38 x + 27

Possible Answers:

$\left( \frac{44}{65} , \frac{529}{40} \right)$

$\left( \frac{44}{65} , - \frac{131}{80} \right)$

$\left( \frac{29}{80} , \frac{529}{40} \right)$

$\left( \frac{44}{65} , 29 \right)$

$\left( - \frac{21}{19} , \frac{529}{40} \right)$

Correct answer:

$\left( \frac{29}{80} , \frac{529}{40} \right)$

Explanation:

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

42 x - 2 = - 38 x + 27

Now we add to each side.

42 x = - 38 x + 29

Now we add 38 x to each side.

80 x = 29

Now we divide by on each side.

$x = \frac{29}{80}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = 42 \cdot \frac{29}{80} -2$

$y = \frac{609}{40} -2$

$y = \frac{529}{40}$

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Example Question #173 : Reasoning With Equations & Inequalities

Where do the following equations intersect?

y = 41 x + 7

y = - x + 27

Possible Answers:

$\left( -41 , \frac{557}{21} \right)$

$\left( \frac{17}{14} , 74 \right)$

$\left( \frac{17}{14} , \frac{157}{21} \right)$

$\left( \frac{10}{21} , \frac{557}{21} \right)$

$\left( \frac{17}{14} , \frac{557}{21} \right)$

Correct answer:

$\left( \frac{10}{21} , \frac{557}{21} \right)$

Explanation:

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

41 x + 7 = - x + 27

Now we subtract from each side.

41 x = - x + 20

Now we add to each side.

42 x = 20

Now we divide by on each side.

$x = \frac{10}{21}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = 41 \cdot \frac{10}{21} + 7$

$y = \frac{410}{21} + 7$

$y = \frac{557}{21}$

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Example Question #174 : Reasoning With Equations & Inequalities

Where do the following equations intersect?

y = - 43 x - 14

y = 27 x - 8

Possible Answers:

$\left( - \frac{43}{27} , - \frac{361}{35} \right)$

$\left( - \frac{3}{35} , - \frac{361}{35} \right)$

$\left( \frac{29}{35} , - \frac{493}{35} \right)$

$\left( \frac{29}{35} , - \frac{361}{35} \right)$

$\left( \frac{29}{35} , -38 \right)$

Correct answer:

$\left( - \frac{3}{35} , - \frac{361}{35} \right)$

Explanation:

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

- 43 x - 14 = 27 x - 8

Now we add to each side.

- 43 x = 27 x + 6

Now we subtract 27 x from each side.

- 70 x = 6

Now we divide by on each side.

$x = - \frac{3}{35}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = -43 \cdot - \frac{3}{35} -14$

$y = \frac{129}{35} -14$

$y = - \frac{361}{35}$

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Example Question #175 : Reasoning With Equations & Inequalities

Where do the following equations intersect?

y = - 8 x - 43

y = - 7 x + 26

Possible Answers:

$\left( \frac{35}{33} , 509 \right)$

$\left( -69 , 509 \right)$

$\left( \frac{8}{7} , 509 \right)$

$\left( \frac{35}{33} , -32 \right)$

$\left( \frac{35}{33} , -112 \right)$

Correct answer:

$\left( -69 , 509 \right)$

Explanation:

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

- 8 x - 43 = - 7 x + 26

Now we add to each side.

- 8 x = - 7 x + 69

Now we add 7 x to each side.

- x = 69

Now we divide by on each side.

x = -69

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = -8 \cdot -69 -43$

y = 552 -43

y = 509

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Example Question #1 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Is the point $\left( 22 , 720 \right)$ included in the inequality $y \geq 10 x^{9}?$

Possible Answers:

Yes

Correct answer:

Explanation:

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ and values.

$720 \geq 10 \cdot 22 ^{9}$

$720 \geq 10 \cdot 1207269217792$

$720 \geq 12072692177920$

Since 720 is not greater than or equal to 12072692177920 the point is not included in the inequality.

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Example Question #2 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Is the point $\left( 1 , -965 \right)$ included in the inequality $y \geq - 33 x^{6}?$

Possible Answers:

Yes

Correct answer:

Explanation:

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ and values.

$-965 \geq -33 \cdot 1 ^{6}$

$-965 \geq -33 \cdot 1$

$-965 \geq -33$

Since is not greater than or equal to the point is not included in the inequality.

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Example Question #3 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Is the point $\left( 42 , -318 \right)$ included in the inequality $y \geq 30 x^{4}?$

Possible Answers:

Yes

Correct answer:

Explanation:

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ and values.

$-318 \geq 30 \cdot 42 ^{ 4 }$

$-318 \geq 30 \cdot 3111696$

$-318 \geq 93350880$

Since is not greater than or equal to 93350880 the point is not included in the inequality.

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Example Question #4 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Is the point $\left( 9 , -705 \right)$ included in the inequality $y \geq 17 x^{11}?$

Possible Answers:

Yes

Correct answer:

Explanation:

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ and values.

$-705 \geq 17 \cdot 9 ^{ 11 }$

$-705 \geq 17 \cdot 31381059609$

$-705 \geq 533478013353$

Since is not greater than or equal to 533478013353 the point is not included in the inequality.

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Example Question #5 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Is the point $\left( 37 , -448 \right)$ included in the inequality $y \geq 3 x^{7}?$

Possible Answers:

Yes

Correct answer:

Explanation:

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ and values.

$-448 \geq 3 \cdot 37 ^{ 7 }$

$-448 \geq 3 \cdot 94931877133$

$-448 \geq 284795631399$

Since is not greater than or equal to 284795631399 the point is not included in the inequality.

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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 #171 : Reasoning With Equations & Inequalities

Example Question #172 : Reasoning With Equations & Inequalities

Example Question #173 : Reasoning With Equations & Inequalities

Example Question #174 : Reasoning With Equations & Inequalities

Example Question #175 : Reasoning With Equations & Inequalities

Example Question #1 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Example Question #2 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Example Question #3 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Example Question #4 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Example Question #5 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

All Common Core: High School - Algebra Resources

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