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Algebra II : Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #24 : How To Find The Solution For A System Of Equations

What is the sum of and for the following system of equations?

3x - 5y = 5

-2x + 5y = 0

Possible Answers:

Correct answer:

Explanation:

3x - 5y = 5

-2x + 5y = 0

Add the equations together.

3x+(-2x)=x

-5y+5y=0

5+0=5

Put the terms together to see that $x+0=5\ \textup{or}\ x=5$ .

Substitute this value into one of the original equaitons and solve for .

3x - 5y = 5

3(5) - 5y = 5

-5y=-10

y=2

Now we know that $x=5\ \textup{and}\ y=2$ , thus we can find the sum of and .

x+y=5+2=7

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Example Question #41 : Solving Equations

Solve for :

6x-3-4x+5=3(x-1)

Possible Answers:

Correct answer:

Explanation:

Combine like terms on the left side of the equation: 2x+2=3(x-1)

Use the distributive property to simplify the right side of the equation: 2x+2=3x-3

Next, move the 's to one side and the integers to the other side: x=5

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Example Question #41 : Solving Equations

Solve for :

ex+f=g

Possible Answers:

$\frac{e}{g-f}$

$\frac{e}{g+f}$

$\frac{g+f}{e}$

None of the other answers

$\frac{g-f}{e}$

Correct answer:

$\frac{g-f}{e}$

Explanation:

To solve for , you must isolate it so that all of the other variables are on the other side of the equation. To do this, first subtract from both sides to get ex=g-f . Then, divide both sides by to get $x=\frac{g-f}{e}$ .

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Example Question #41 : Solving Equations

3x+12=36 , solve for .

Possible Answers:

Correct answer:

Explanation:

First you need to subtract 12 from both sides of the equation:

3x+12-12=36-12.

This gives us

3x=24.

Then, divide each side by 3:

$\frac{3x}{3}=\frac{24}{3}$ which, when simplified, gives us:

x=8.

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Example Question #42 : Solving Equations

Solve for :

$\frac{x}{4} - 3x = 121$

Possible Answers:

x = -11

None of the other answers.

x = 11

x = 44

x = -44

Correct answer:

x = -44

Explanation:

$\frac{x}{4} - 3x = 121$

Step 1: Multiply both sides of the equation by 4.

$\rightarrow x - 12x = 484$

Step 2: Combine the 's.

$\rightarrow -11x = 484$

Step 3: Divide both sides of the equation by -11.

$\rightarrow x = -44$

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Example Question #43 : Solving Equations

Solve for :

$15 + \frac{y}{2} = 20 - 5y$

Possible Answers:

$y = -\frac{3}{5}$

None of the other answers.

$y = \frac{11}{10}$

$y = \frac{10}{11}$

$y = -\frac{5}{3}$

Correct answer:

$y = \frac{10}{11}$

Explanation:

$15 + \frac{y}{2} = 20 - 5y$

Step 1: Multiply both sides of the equation by 2.

$\rightarrow 30 + y = 40 - 10 y$

Step 2: Add 10y to both sides of the equation, and subtract 30 from both sides of the equation.

$\rightarrow 11y = 10$

Step 3: Divide both sides of the equation by 11.

$\rightarrow y = \frac{10}{11}$

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Example Question #44 : Solving Equations

Solve for :

$20 + \frac{2x}{3} = 100$

Possible Answers:

x = 140

x = 50

x = 120

x = 180

None of the other answers.

Correct answer:

x = 120

Explanation:

$20 + \frac{2x}{3} = 100$

Step 1: Multiply both sides of the equation by 3.

$\rightarrow 60 + 2x = 300$

Step 2: Subtract 60 from both sides of the equation.

$\rightarrow 2x = 240$

Step 3: Divide both sides of the equation by 2.

$\rightarrow x = 120$

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Example Question #45 : Solving Equations

Solve for :

$\frac{x}{5} - 22 = -10$

Possible Answers:

x = 28

x = 60

x = -60

None of the other answers.

x = 160

Correct answer:

x = 60

Explanation:

$\frac{x}{5} - 22 = -10$

Step 1: Multiply both sides of the equation by 5.

$\rightarrow x - 110 = -50$

Step 2: Add 110 to both sides of the equation.

$\rightarrow x = 60$

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Example Question #45 : Solving Equations

Solve for :

$-16 - 4x = \frac{x}{5} + 2x$

Possible Answers:

None of the other answers.

$x = -\frac{31}{80}$

$x = \frac{80}{31}$

$x = -\frac{80}{23}$

$x = - \frac{80}{31}$

Correct answer:

$x = - \frac{80}{31}$

Explanation:

$-16 - 4x = \frac{x}{5} + 2x$

Step 1: Multiply both sides of the equation by 5.

$\rightarrow -80 - 20x = x + 10x$

Step 2: Combine the 's.

$\rightarrow -80 - 20x = 11x$

Step 3: Add 20x to both sides of the equation.

$\rightarrow -80 = 31x$

Step 4: Divide both sides of the equation by 31.

$\rightarrow x = -\frac{80}{31}$

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Example Question #48 : Solving Equations

Solve for :

$48 = \frac{x}{2} + 20$

Possible Answers:

x = 76

None of the other answers.

x = 136

x = 56

x = -56

Correct answer:

x = 56

Explanation:

$48 = \frac{x}{2}+ 20$

Step 1: Multiply both sides of the equation by 2.

$\rightarrow 96 = x + 40$

Step 2: Subtract 40 from both sides of the equation.

$\rightarrow x = 56$

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Algebra II : Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #24 : How To Find The Solution For A System Of Equations

Example Question #41 : Solving Equations

Example Question #41 : Solving Equations

Example Question #41 : Solving Equations

Example Question #42 : Solving Equations

Example Question #43 : Solving Equations

Example Question #44 : Solving Equations

Example Question #45 : Solving Equations

Example Question #45 : Solving Equations

Example Question #48 : Solving Equations

All Algebra II Resources

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