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Algebra 1 : How to find the solution to a binomial problem

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Example Questions

Example Question #1 : How To Find The Solution To A Binomial Problem

Solve for : (x+5)+(3x+15)=0

Possible Answers:

$\frac{20}{3}$

Correct answer:

Explanation:

First, rearrange the equation so that "like terms" are grouped together, like this: 1x+3x+5+15 .

Second, combine "like" terms with the appropriate mathematical function (i.e., addition, subtraction, etc.), so in this problem, you'll be left with 4x+20 .

Third, set the entire equation equal to and solve for :

4x+20=0

4x=-20

$\frac{4x}{4}=\frac{-20}{4}$

x=-5

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Example Question #2 : How To Find The Solution To A Binomial Problem

Solve for : (x-3)+(3x-2)=7 .

Possible Answers:

$\frac{1}{2}$

Correct answer:

Explanation:

First, rearrange the equation so that "like terms" are grouped together, like this: 1x+3x-3-2 .

Second, combine "like" terms with the appropriate mathematical function (i.e., addition, subtraction, etc.), so in this problem, you'll be left with

4x-5=7 .

Third, solve for :

4x-5=7

4x=12

$\frac{4x}{4}=\frac{12}{4}$

x=3

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Example Question #2 : Finding Roots

Solve for :

(x+3)^2=16

Possible Answers:

x=1

$x=4\ or\ x=-4$

x=-4

$x=1\ or\ x=-7$

Correct answer:

$x=1\ or\ x=-7$

Explanation:

(x+3)^2=16

$\sqrt{(x+3)^2}=\sqrt{16}\textup{}$

$x+3=\pm4$

$x=1\ or\ -7$

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Example Question #1 : How To Find The Solution To A Binomial Problem

4x-8y=32

Solve for in terms of .

Possible Answers:

x=8-2y

y=4-0.5x

x = 8 + 2y

y=0.5x-4

Correct answer:

x = 8 + 2y

Explanation:

First, add 8y to both sides of the equation, cancelling out -8y and isolating x to a value in terms of y:

4x - 8y = 32

+8y +8y

4x = 32 + 8y

Then divide both sides of the equation by 4, providing the x-value in terms of y:

x = 8 + 2y

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Example Question #3 : How To Find The Solution To A Binomial Problem

Solve in terms of :

$\frac{2}{3}x+5y=7$

Possible Answers:

$x=7+\frac{10}{3}y$

$x=7-\frac{10}{3}y$

$x=\frac{21}{2}-\frac{15}{2}y$

$x=\frac{21}{2}+\frac{15}{2}y$

Correct answer:

$x=\frac{21}{2}-\frac{15}{2}y$

Explanation:

First, isolate X by itself:

$\frac{2}{3}x+5y=7$

-5y -5y

$\frac{2}{3}x=7-5y$

Next, divide both sides by 2/3 to get X by itself:

$\frac{2}{3}\div\frac{2}{3}x=\frac{2}{3}\div\frac{7}{1}-\frac{2}{3}\div\frac{5}{1}y$

$\frac{3}{2}\cdot\frac{2}{3}x=\frac{3}{2}\cdot\frac{7}{1}-\frac{3}{2}\cdot\frac{5}{1}y$

Your answer should come out as:

$x=\frac{21}{2}-\frac{15}{2}y$

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Example Question #1 : How To Find The Solution To A Binomial Problem

Solve for in terms of :

$\frac{4}{3}x-3=\frac{2}{9}y$

Possible Answers:

$x=\frac{8}{27}y-3$

$x=\frac{-8}{27}y+3$

$x=\frac{1}{6}y-\frac{9}{4}$

$x=\frac{1}{6}y+\frac{9}{4}$

$x=\frac{8}{27}y+3$

Correct answer:

$x=\frac{1}{6}y+\frac{9}{4}$

Explanation:

First, isolate X onto one side of the equation:

$\frac{4}{3}X-3=\frac{2}{9}Y$

$\frac{4}{3}X=\frac{2}{9}Y+3$

Next, divide both sides of the equation by 4/3:

$\frac{4}{3}\div \frac{4}{3}X=\frac{4}{3}\div \frac{2}{9}Y+\frac{4}{3}\div \frac{3}{1}$

$\frac{3}{4}\cdot \frac{4}{3}X=\frac{3}{4}\cdot \frac{2}{9}Y+\frac{3}{4}\cdot \frac{3}{1}$

$X=\frac{6}{36}Y+\frac{9}{4}$

When simplified, your answer should be:

$X=\frac{1}{6}Y+\frac{9}{4}$

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Example Question #1 : How To Find The Solution To A Binomial Problem

Solve for

-1 = 6 + x

Possible Answers:

Correct answer:

Explanation:

-1 = 6 + x

-1-6 = 6+x-6

-7 = x

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Example Question #3 : How To Find The Solution To A Binomial Problem

Solve for

3 = -6 + x

Possible Answers:

Correct answer:

Explanation:

$\\3 = -6 + x \\3 + 6 = -6 + x + 6 \\9 = x$

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Example Question #3 : How To Find The Solution To A Binomial Problem

Solve for

3 = 2 - x

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

$\\3 = 2 - x \\3 - 2 = 2 - x - 2\\ 1 = -x(-1) = x$

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Example Question #1 : How To Find The Solution To A Binomial Problem

Solve for

19 = 7 + x

Possible Answers:

Correct answer:

Explanation:

$\\19 = 7 + x \\ 19 - 7 = 7 + x -7 \\ 12 = x$

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Algebra 1 : How to find the solution to a binomial problem

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Find The Solution To A Binomial Problem

Example Question #2 : How To Find The Solution To A Binomial Problem

Example Question #2 : Finding Roots

Example Question #1 : How To Find The Solution To A Binomial Problem

Example Question #3 : How To Find The Solution To A Binomial Problem

Example Question #1 : How To Find The Solution To A Binomial Problem

Example Question #1 : How To Find The Solution To A Binomial Problem

Example Question #3 : How To Find The Solution To A Binomial Problem

Example Question #3 : How To Find The Solution To A Binomial Problem

Example Question #1 : How To Find The Solution To A Binomial Problem

All Algebra 1 Resources

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