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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 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Solve for .

x+2x+1=8+4x

Possible Answers:

x=7

x=-6

x=9

x=-9

x=-7

Correct answer:

x=-7

Explanation:

To solve for , first combine like terms.

x+2x+1=8+4x

On the left-hand side of the equation there are two terms that contain . Therefore, add and together.

3x+1=8+4x

Now, move the term from the left-hand side to the right-hand side. To accomplish this, subtract from both sides.

3x+1=8+4x

-3x -3x

_____________________

1=8+x

Next, to isolate , subtract the constant from the right-hand side of the equation to the left-hand side.

1=8+x

______________

-7=x

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Example Question #2 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Solve for .

3x-2x+1=8+4x

Possible Answers:

$x=\frac{3}{7}$

$x=\frac{7}{3}$

$x=-\frac{3}{7}$

$x=-\frac{7}{3}$

x=-21

Correct answer:

$x=-\frac{7}{3}$

Explanation:

To solve for , first combine like terms.

3x-2x+1=8+4x

On the left-hand side of the equation there are two terms that contain . Therefore, subtract from .

x+1=8+4x

Now, move the term from the left-hand side to the right-hand side. To accomplish this, subtract from both sides.

x+1=8+4x

_____________________

1=8+3x

Next, subtract the constant from the right-hand side of the equation to the left-hand side.

1=8+3x

______________

-7=3x

Finally divide each side by three to solve for .

$\\\frac{-7}{3}=\frac{3x}{3} \\\\-\frac{7}{3}=x$

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Example Question #3 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Solve for .

x+2x+3=8+4x

Possible Answers:

x=24

x=5

x=-5

x=11

x=-11

Correct answer:

x=-5

Explanation:

To solve for , first combine like terms.

x+2x+3=8+4x

On the left-hand side of the equation there are two terms that contain . Therefore, add and together.

3x+3=8+4x

Now, move the term from the left-hand side to the right-hand side. To accomplish this, subtract from both sides.

3x+3=8+4x

-3x -3x

_____________________

3=8+x

Next, to isolate , subtract the constant from the right-hand side of the equation to the left-hand side.

3=8+x

______________

-5=x

Report an Error

Example Question #4 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Solve for .

x+2x+12=8+4x

Possible Answers:

x=20

x=3

x=-4

x=8

x=4

Correct answer:

x=4

Explanation:

To solve for , first combine like terms.

x+2x+12=8+4x

On the left-hand side of the equation there are two terms that contain . Therefore, add and together.

3x+12=8+4x

Now, move the term from the left-hand side to the right-hand side. To accomplish this, subtract from both sides.

3x+12=8+4x

-3x -3x

_____________________

12=8+x

Next, to isolate , subtract the constant from the right-hand side of the equation to the left-hand side.

12=8+x

______________

4=x

Report an Error

Example Question #1 : Reasoning With Equations & Inequalities

Solve for .

x+2x+12=9+4x

Possible Answers:

x=-3

x=4

x=21

x=3

x=6

Correct answer:

x=3

Explanation:

To solve for , first combine like terms.

x+2x+12=9+4x

On the left-hand side of the equation there are two terms that contain . Therefore, add and together.

3x+12=9+4x

Now, move the term from the left-hand side to the right-hand side. To accomplish this, subtract from both sides.

3x+12=9+4x

-3x -3x

_____________________

12=9+x

Next, to isolate , subtract the constant from the right-hand side of the equation to the left-hand side.

12=9+x

______________

3=x

Report an Error

Example Question #2 : Reasoning With Equations & Inequalities

Solve for .

x-3x+1=x+4

Possible Answers:

x=4

x=-1

x=6

x=-3

x=1

Correct answer:

x=-1

Explanation:

To solve for , first combine the like terms on the left-hand side of the equation.

x-3x+1=x+4

x-3x=-2x

Therefore, the equation becomes,

-2x+1=x+4

Now, move all the variables to the right-hand side of the equation by adding to both sides.

-2x+1=x+4

+2x +2x

____________________

1=3x+4

From here, subtract the constant on the right-hand side from both sides of the equation.

1=3x+4

_______________

-3=3x

Lastly, divide by three on both sides of the equation to solve for .

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

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Example Question #2 : Reasoning With Equations & Inequalities

Solve for .

$\frac{x}{2}+1=3$

Possible Answers:

x=2

x=4

x=1

x=-4

x=-2

Correct answer:

x=4

Explanation:

To solve for , first subtract one from both sides to combine the constant terms.

$\frac{x}{2}+1=3$

____________

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

From here, multiply by two on both sides to solve for .

$\\2\times \frac{x}{2}=2\times 2 \\\\x=4$

The two in the numerator cancels the two in the denominator on the left-hand side of the equation; thus, isolating .

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Example Question #1 : Reasoning With Equations & Inequalities

Solve for .

$\frac{x}{3}-2=6$

Possible Answers:

x=20

x=14

x=24

x=12

x=36

Correct answer:

x=24

Explanation:

To solve for first combine the constant terms by adding two to both sides of the equation.

$\frac{x}{3}-2=6$

_____________

$\frac{x}{3}=8$

From here, multiply each side of the equation by 3 to solve for .

$3\cdot \frac{x}{3}=8\cdot 3$

The three in the numerator cancels out the three in the denominator on the left-hand side of the equation; thus, solving for .

x=24

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Example Question #7 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Solve for .

3x-2x=7+3+2x

Possible Answers:

x=-12

x=10

x=16

x=12

x=-10

Correct answer:

x=-10

Explanation:

First, combine like terms on both sides of the equation.

3x-2x=7+3+2x

On the left-hand side:

$\\3x-2x=x \\7+3=10$

Thus the equation becomes,

x=10+2x

Now, subtract from both sides.

x=10+2x

-2x -2x

__________________

-x=10

Lastly, divide by negative one on both sides.

$\frac{-x}{-1}=\frac{10}{-1}$

x=-10

Report an Error

Example Question #8 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Solve for .

2x-10=x+7

Possible Answers:

x=17

x=-3

x=70

x=-70

x=3

Correct answer:

x=17

Explanation:

First, subtract from both sides to get the variables on one side.

2x-10=x+7

____________________

x-10=7

From here, add ten to both sides to get all constants on one side, and solve for .

x-10=7

+10 +10

_______________

x=17

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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 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Example Question #2 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Example Question #3 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Example Question #4 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Example Question #1 : Reasoning With Equations & Inequalities

Example Question #2 : Reasoning With Equations & Inequalities

Example Question #2 : Reasoning With Equations & Inequalities

Example Question #1 : Reasoning With Equations & Inequalities

Example Question #7 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Example Question #8 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

All Common Core: High School - Algebra Resources

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