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Algebra II : Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #740 : Basic Single Variable Algebra

Solve the equation: 8x = 3(5-x)

Possible Answers:

$\frac{15}{11}$

$-\frac{3}{8}$

$\frac{11}{15}$

$-\frac{11}{15}$

Correct answer:

$\frac{15}{11}$

Explanation:

Simplify the right side of the equation by distribution.

8x = 15-3x

Add on both sides.

8x+3x = 15-3x+3x

The equation becomes:

8x+3x = 15

Combine like terms.

11x=15

Divide by 11 on both sides.

$\frac{11x}{11}=\frac{15}{11}$

The answer is: $\frac{15}{11}$

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Example Question #261 : Solving Equations

Solve the equation: 81-2x = 9(x+2)

Possible Answers:

$\frac{83}{7}$

$\frac{99}{7}$

$\frac{63}{11}$

Correct answer:

$\frac{63}{11}$

Explanation:

Use distribution to simplify the right side.

81-2x = 9(x)+9(2)

81-2x = 9x+18

Add on both sides.

81-2x +2x= 9x+18+2x

81= 11x+18

Subtract 18 from both sides.

81-18= 11x+18-18

63= 11x

Divide by 11 on both sides.

$\frac{63}{11}= \frac{11x}{11}$

The answer is: $\frac{63}{11}$

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Example Question #392 : Equations

Given the set of equations, solve for : $\begin{Bmatrix} x-3y= 8\\x+9y=7 \end{Bmatrix}$

Possible Answers:

$\frac{31}{4}$

$\textup{No solution.}$

$-\frac{1}{12}$

Correct answer:

$\frac{31}{4}$

Explanation:

In order to solve for the x-variable, we will need use the elimination method to cancel the y-terms.

Multiply the first equation by three, so that we can use addition to turn two equations into one.

$\begin{Bmatrix} x-3y= 8\\x+9y=7 \end{Bmatrix} \rightarrow\begin{Bmatrix} 3[x-3y= 8]\\x+9y=7 \end{Bmatrix}\rightarrow \begin{Bmatrix} 3x-9y= 24\\x+9y=7 \end{Bmatrix}$

Adding the converted equations together will cancel out the terms, and will leave the x-variable by themselves. The two equations will become one equation after adding.

4x=31

Divide by four on both sides.

The answer is: $\frac{31}{4}$

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Example Question #393 : Equations

Solve the following equation: 9(-x+9)= -34

Possible Answers:

$-\frac{115}{9}$

$-\frac{47}{9}$

$\frac{35}{3}$

$\frac{47}{9}$

$\frac{115}{9}$

Correct answer:

$\frac{115}{9}$

Explanation:

Distribute the nine through the binomial.

9(-x)+9(9)= -34

Simplify the terms.

-9x+81 = -34

Subtract 81 from both sides.

-9x+81 -81= -34-81

-9x= -115

Divide by negative nine on both sides. The negatives will cancel.

The answer is: $\frac{115}{9}$

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Example Question #394 : Equations

Solve: -8x-24=-(2-9x)

Possible Answers:

$-\frac{22}{17}$

$-\frac{20}{17}$

$-\frac{24}{17}$

Correct answer:

$-\frac{22}{17}$

Explanation:

Simplify the right side by distributing the negative sign through the binomial.

-8x-24=-2+9x

Subtract from both sides.

-8x-24-9x=-2+9x-9x

-17x-24=-2

Add 24 on both sides.

-17x-24+24=-2+24

-17x = 22

Divide by negative 17 on both sides.

The answer is: $-\frac{22}{17}$

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Example Question #395 : Equations

Solve: 8x-3= 7-8x

Possible Answers:

$\frac{5}{4}$

$\textup{No solution.}$

$\frac{1}{4}$

$\frac{7}{8}$

$\frac{5}{8}$

Correct answer:

$\frac{5}{8}$

Explanation:

Add on both sides.

8x-3+8x= 7-8x+8x

Simplify both sides.

16x-3 =7

Add three on both sides.

16x-3+3 =7+3

16x=10

Divide both sides by 16.

$\frac{16x}{16}=\frac{10}{16}$

Simplify both sides.

The answer is: $\frac{5}{8}$

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Example Question #396 : Equations

Solve the equation: -9x+18 = -32+3x

Possible Answers:

$\frac{25}{3}$

$\frac{50}{3}$

$\frac{25}{6}$

Correct answer:

$\frac{25}{6}$

Explanation:

Subtract from both sides.

-9x+18 -3x= -32+3x-3x

-12x+18 = -32

Subtract 18 from both sides.

-12x+18 -18= -32-18

-12x =-50

Divide by negative 12 on both sides.

$\frac{-12x}{-12} =\frac{-50}{-12}$

Reduce the fractions.

The answer is: $\frac{25}{6}$

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Example Question #397 : Equations

Solve: $\frac{1}{2x}-3 = 9$

Possible Answers:

$\frac{1}{4}$

$\frac{1}{12}$

$\frac{1}{6}$

$\frac{1}{24}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{24}$

Explanation:

Add three on both sides.

$\frac{1}{2x}-3+3 = 9+3$

$\frac{1}{2x}=12$

Multiply by on both sides.

$\frac{1}{2x}\cdot 2x=12\cdot2x$

1=24x

Divide by 24 on both sides.

$\frac{1}{24}=\frac{24x}{24}$

The answer is: $\frac{1}{24}$

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Example Question #398 : Equations

Solve the equation: 3(x-9)=-63

Possible Answers:

Correct answer:

Explanation:

Divide by three on both sides.

$\frac{3(x-9)}{3}=\frac{-63}{3}$

The equation becomes:

x-9 =-21

Add nine on both sides.

x-9 +9=-21+9

x=-12

The answer is:

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Example Question #399 : Equations

Solve the equation: -9(x-3)=6-x

Possible Answers:

$\frac{8}{3}$

$-\frac{33}{10}$

$\frac{19}{8}$

$\frac{21}{8}$

$\frac{21}{38}$

Correct answer:

$\frac{21}{8}$

Explanation:

Use distribution to expand the left side of the equation.

-9(x)-(-9)(3)=6-x

-9x+27 = 6-x

Add on both sides.

-9x+27 +9x= 6-x+9x

27=6+8x

Subtract six from both sides.

27-6=6+8x-6

21=8x

Divide by eight on both sides.

The answer is: $\frac{21}{8}$

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Algebra II : Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #740 : Basic Single Variable Algebra

Example Question #261 : Solving Equations

Example Question #392 : Equations

Example Question #393 : Equations

Example Question #394 : Equations

Example Question #395 : Equations

Example Question #396 : Equations

Example Question #397 : Equations

Example Question #398 : Equations

Example Question #399 : Equations

All Algebra II Resources

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