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Algebra II : Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #9 : Simplifying Equations

Solve for : 2x(y+z)+5 = 7-x

Possible Answers:

$x= \frac{2}{2y+2z+1}$

$x=\frac{2-y-z}{3}$

$x=\frac{2-x}{2y+2z}$

$x= \frac{2}{2y+2z-1}$

$x=\frac{2}{3y+3z}$

Correct answer:

$x= \frac{2}{2y+2z+1}$

Explanation:

In order to isolate the variable, we will need to use order of operations to eliminate the parentheses and group the terms with an variable to one side of the equation.

Distribute inside the parentheses.

2xy+2xz+5 = 7-x

Subtract five on both sides.

2xy+2xz= 2-x

Add on both sides to move the negative to the left side.

2xy+2xz+x= 2

Take out a common factor of on the left side.

x(2y+2z+1)= 2

Divide by 2y+2z+1 on both sides of the equation.

The answer is: $x= \frac{2}{2y+2z+1}$

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Example Question #10 : Simplifying Equations

Simplify:

$\frac{2x^{2}+24x}{2x}$

Possible Answers:

2x+12

x+12

$\frac{2x+24}{2}$

x+24x

Correct answer:

x+12

Explanation:

To simplify:

$\frac{2x^{2}+24x}{2x}$

1. Factor out from $2x^{2}+24x$ and we will get:

$\frac{2x(x+12)}{2x}$

2. Reduce the equation and the final solution is:

x+12

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Example Question #471 : Basic Single Variable Algebra

Simplify:

$\frac{25x^{2}y^{3}}{20x^{2}y^{6}}$

Possible Answers:

$\frac{5}{4y^{2}}$

$\frac{5y^{3}}{4}$

$\frac{5y^{3}}{4y^{6}}$

$\frac{5}{4y^{3}}$

$\frac{4y^{3}}{5}$

Correct answer:

$\frac{5}{4y^{3}}$

Explanation:

To simplify the equation you need to divide the numerator (top) and denominator (bottom), so:

The numerator can be factored to:

5*5*x*x*y*y*y

The denominator can be factored to:

4*5*x*x*y*y*y*y*y*y

$\frac{5*5*x*x*y*y*y}{4*5*x*x*y*y*y*y*y*y}$

After reducing, we will get

$\frac{5}{4*y*y*y} = \frac{5}{4y^{3}}$

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Example Question #471 : Basic Single Variable Algebra

Simplify:

$\frac{4x^{2}}{2x}$

Possible Answers:

$\frac{4x}{2}$

Correct answer:

Explanation:

To simplify the equation you need to divide the numerator (top) and denominator (bottom), so:

The numerator can be factored to:

2*2*x*x

The denominator can be factored to:

2*x

$\frac{2*2*x*x}{2*x}$

After reducing, we will get

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Example Question #2311 : Algebra Ii

Solve for : $\frac{x(x^3+3y)}{x+2} = 2x$

Possible Answers:

$y=-\frac{1}{3}x^3+\frac{2}{3}x+\frac{4}{3}$

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

$y=\frac{1}{3}x^3+\frac{2}{3}x+\frac{4}{3}$

$y=-\frac{1}{3}x^3-\frac{2}{3}x-\frac{4}{3}$

$y=-\frac{1}{3}x^4+\frac{2}{3}x^2+\frac{4}{3}x$

Correct answer:

$y=-\frac{1}{3}x^3+\frac{2}{3}x+\frac{4}{3}$

Explanation:

Multiply x+2 on both sides in order to eliminate the denominator.

$\frac{x(x^3+3y)}{x+2} \cdot (x+2)= 2x\cdot (x+2)$

Simplify both sides.

x(x^3+3y) = 2x(x+2)

Use distribution to simplify both sides.

x^4+3xy = 2x^2+4x

Isolate the term with only the y-variable by subtracting x^4 on both sides.

x^4+3xy -x^4= 2x^2+4x-x^4

Simplify and reorder the right side by the order of power.

3xy = -x^4+2x^2+4x

Divide by on both sides.

$\frac{3xy}{3x} = \frac{-x^4+2x^2+4x}{3x}$

Simplify both sides.

The answer is: $y=-\frac{1}{3}x^3+\frac{2}{3}x+\frac{4}{3}$

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Example Question #2314 : Algebra Ii

Simplify the equation: 6(2x-3)=-48

Possible Answers:

$-\frac{11}{2}$

$-\frac{2}{11}$

$-\frac{3}{2}$

$-\frac{5}{2}$

$-\frac{2}{5}$

Correct answer:

$-\frac{5}{2}$

Explanation:

In order to simplify and solve this equation, divide by six on both sides.

$\frac{6(2x-3)}{6}=\frac{-48}{6}$

Simplify both sides.

2x-3=-8

Add three on both sides.

2x-3+3=-8+3

Simplify both sides.

2x=-5

Divide both sides by two.

$\frac{2x}{2}=\frac{-5}{2}$

The answer is: $x=-\frac{5}{2}$

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Example Question #2315 : Algebra Ii

Simplify the following equation: 3x+9 = -57

Possible Answers:

Correct answer:

Explanation:

Subtract nine from both sides.

3x+9 -9= -57-9

3x=-66

Divide both sides.

$\frac{3x}{3}=\frac{-66}{3}$

x=-22

The answer is:

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Example Question #11 : Simplifying Equations

Simplify the equation: 2(3x-2) -38= 0

Possible Answers:

$\frac{1}{7}$

$\frac{17}{3}$

$-\frac{17}{3}$

Correct answer:

Explanation:

Add 38 on both sides.

2(3x-2) -38+38= 0+38

2(3x-2)=38

Divide by two on both sides.

$\frac{2(3x-2) }{2}= \frac{38}{2}$

The equation becomes:

3x-2 = 19

Add two on both sides.

3x-2 +2= 19+2

3x=21

Divide by three on both sides.

$\frac{3x}{3}=\frac{21}{3}$

The answer is:

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Example Question #2317 : Algebra Ii

Simplify the equation: $(\frac{2}{5}x)^2+\frac{1}{2}x-\frac{2}{5}x-8$

Possible Answers:

$\frac{4}{25}x^2+\frac{1}{10}x-8$

None of the other answers.

$\frac{4}{25}x+\frac{1}{10}x-8$

$\frac{2}{5}x^2+\frac{1}{10}x-8$

$\frac{4}{25}x^2-\frac{3}{7}x-8$

Correct answer:

$\frac{4}{25}x^2+\frac{1}{10}x-8$

Explanation:

$(\frac{2}{5}x)^2+\frac{1}{2}x-\frac{2}{5}x-8$

Start by squaring everything within the parentheses:

$\frac{4}{25}x^2+\frac{1}{2}x-\frac{2}{5}x-8$

Now combine the fractions of degree 1 by finding a common denominator:

$\frac{4}{25}x^2+\frac{5}{5}*\frac{1}{2}x-\frac{2}{2}*\frac{2}{5}x-8$

$\frac{4}{25}x^2+\frac{5}{10}x-\frac{4}{10}x-8\rightarrow \boldsymbol{\frac{4}{25}x^2+\frac{1}{10}x-8}$

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Example Question #121 : Equations

Simplify this expression:

$(4x^{4}-x^{2})+(x^2+5x^4)$

Possible Answers:

$9x^{4}$

$-x^{4}-x^{2}$

3x^2-1

$9x^{4}-2x^{2}$

$x^{4}+x^{2}$

Correct answer:

$9x^{4}$

Explanation:

Drop the parentheses and combine like terms.

$5x^{4}+4x^{4}=9x^{4}$

and

$-x^{2}+x^{2}=0$

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Algebra II : Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #9 : Simplifying Equations

Example Question #10 : Simplifying Equations

Example Question #471 : Basic Single Variable Algebra

Example Question #471 : Basic Single Variable Algebra

Example Question #2311 : Algebra Ii

Example Question #2314 : Algebra Ii

Example Question #2315 : Algebra Ii

Example Question #11 : Simplifying Equations

Example Question #2317 : Algebra Ii

Example Question #121 : Equations

All Algebra II Resources

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