How to find the solution to a binomial problem

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Algebra › How to find the solution to a binomial problem

Questions 1 - 10

1

Solve for in terms of .

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

2

Solve for

Explanation

3

Solve in terms of :

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

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

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

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

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

Explanation

First, isolate X by itself:

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

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

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:

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

4

Solve for in terms of :

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

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

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

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

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

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

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:

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

5

Solve for

None of the other answers.

Explanation

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

6

Solve for :

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

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

Explanation

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

$x+3=\pm4$

$x=1\ or\ -7$

7

Solve for

Explanation

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

8

Solve for

None of the other answers.

Explanation

$\-9 = 82 + x \ -9 - 82 = 82 + x - 82 \-91 = x$

9

Solve for

None of the other answers.

Explanation

$\1 = -3 + x \1 + 3 = -3 + x + 3\ 4 = x$

10

Solve for :

$\frac{20}{3}$

Explanation

First, rearrange the equation so that "like terms" are grouped together, like this: .

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

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

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

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