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Algebra II : Solving Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #231 : Solving Equations

Solve for .

4(x-15)=2(2x-6)

Possible Answers:

No Solutions

Correct answer:

No Solutions

Explanation:

To solve for , we need to isolate the variable by having the variable on one side and numbers on the other side.

4(x-15)=2(2x-6) Distribute the 4,2 to each term in the parentheses.

4x-60=4x-24 Because there is on each side of the equation, they would essentially cancel out leaving us with 0=36 which is not valid.

Answer is no solutions.

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Example Question #232 : Solving Equations

Solve: 9x-17=81-2x

Possible Answers:

$\frac{108}{11}$

$\frac{98}{11}$

$\frac{108}{7}$

$-\frac{98}{11}$

Correct answer:

$\frac{98}{11}$

Explanation:

Isolate the x-variables on one side of the equation and the integers on the other.

Add on both sides of the equation.

9x-17+2x=81-2x+2x

11x-17=81

Add 17 on both sides of the equation.

11x-17+17=81+17

Simplify both sides.

11x=98

Divide by 11 on both sides.

$x=\frac{98}{11}$

The answer is: $\frac{98}{11}$

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Example Question #233 : Solving Equations

Solve the equation: 4(x-9) = 30x

Possible Answers:

$\frac{18}{17}$

$-\frac{18}{13}$

$\frac{3}{2}$

$\frac{18}{13}$

$\frac{33}{2}$

Correct answer:

$-\frac{18}{13}$

Explanation:

Use distribution to simplify the left side.

4(x)-4(9) = 30x

4x-36=30x

Subtract on both sides.

4x-36-(4x)=30x-(4x)

Simplify.

-36 = 26x

Divide by 26 on both sides.

$\frac{-36}{26} = \frac{26x}{26}$

Reduce both fractions.

The answer is: $-\frac{18}{13}$

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Example Question #234 : Solving Equations

Solve the equation: $\frac{10}{11}x - \frac{1}{33} = \frac{7}{66}$

Possible Answers:

$\frac{3}{20}$

$\frac{13}{66}$

$\frac{3}{40}$

$\frac{10}{3}$

Correct answer:

$\frac{3}{20}$

Explanation:

In order to determine the value of x, we will need to convert the fractions to a least common denominator.

The LCD is 66 because this value is the smallest number that every individual denominator can be divided into.

Convert the fractions.

$\frac{10(6)}{11(6)}x - \frac{1(2)}{33(2)} = \frac{7}{66}$

$\frac{60}{66}x-\frac{2}{66}= \frac{7}{66}$

Since all the denominators are similar, we can simply set the numerators equal. Multiplying both sides by 66 will eliminate the denominators.

60x-2=7

Add two on both sides.

60x=9

Divide by 60 on both sides and reduce the fraction.

$\frac{60x}{60}=\frac{9}{60}= \frac{3}{20}$

The answer is: $\frac{3}{20}$

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Example Question #235 : Solving Equations

Solve the equation: 9-18x =43+2x

Possible Answers:

$-\frac{16}{17}$

$-\frac{27}{10}$

$-\frac{17}{8}$

$-\frac{17}{10}$

Correct answer:

$-\frac{17}{10}$

Explanation:

Group the x-variables and integers on a separate side of the equation.

Add 18x on both sides.

9-18x +(18x)=43+2x+(18x)

Simplify the equation.

9=20x+43

Subtract on both sides.

9-43=20x+43-43

Simplify both sides.

-34=20x

Divide by twenty on both sides.

$\frac{-34}{20}=\frac{20x}{20}$

Reduce both fractions.

The answer is: $-\frac{17}{10}$

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Example Question #236 : Solving Equations

Solve the following equation: $\frac{1}{x}+2 =-8$

Possible Answers:

$\frac{3}{5}$

$-\frac{1}{60}$

$-\frac{1}{6}$

$-\frac{1}{10}$

$-\frac{1}{16}$

Correct answer:

$-\frac{1}{10}$

Explanation:

Subtract two from both sides.

$\frac{1}{x}+2-2 =-8-2$

$\frac{1}{x}=-10$

Multiply by on both sides.

$\frac{1}{x} \cdot x=-10 \cdot x$

1=-10x

Divide by negative ten on both sides.

$\frac{1}{-10}=\frac{-10x}{-10}$

Simplify both fractions.

The answer is: $-\frac{1}{10}$

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Example Question #237 : Solving Equations

Solve the equation: -7x+38 = -5x-50

Possible Answers:

$-\frac{22}{3}$

$\frac{22}{3}$

Correct answer:

Explanation:

Isolate the x-variables on one side and the integers on another.

Add on both sides of the equation.

-7x+38 +(7x)= -5x-50+(7x)

Simplify both sides.

38= 2x-50

Add 50 on both sides.

38+50= 2x-50+50

88=2x

Divide by two on both sides.

$\frac{88}{2}=\frac{2x}{2}$

The answer is:

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Example Question #238 : Solving Equations

Solve the equation: 9x-6=3x+4

Possible Answers:

$\frac{5}{3}$

$\frac{5}{2}$

$\frac{1}{3}$

$-\frac{3}{5}$

$\textup{The answer is not given.}$

Correct answer:

$\frac{5}{3}$

Explanation:

Subtract from both sides.

9x-6-(3x)=3x+4-(3x)

6x-6=4

Add six on both sides.

6x-6+6=4+6

6x=10

Divide by six on both sides.

$\frac{6x}{6}=\frac{10}{6}$

Reduce the fractions.

The answer is: $\frac{5}{3}$

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Example Question #239 : Solving Equations

Solve the equation: -4x-18 = 46-8x

Possible Answers:

$-\frac{16}{7}$

$-\frac{16}{3}$

Correct answer:

Explanation:

Add on each side.

-4x-18 +8x= 46-8x+8x

Simplify both sides.

4x-18= 46

Add 18 on both sides.

4x-18+18= 46+18

4x=64

Divide four on both sides.

$\frac{4x}{4}=\frac{64}{4}$

The answer is:

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Example Question #231 : Solving Equations

Solve the equation: 6x-18 = 3x-2

Possible Answers:

$\frac{16}{3}$

$\textup{The answer is not given.}$

$-\frac{16}{3}$

$\frac{20}{3}$

Correct answer:

$\frac{16}{3}$

Explanation:

Subtract on both sides.

6x-18 -3x= 3x-2-3x

3x-18 = -2

Add 18 on both sides.

3x-18 +18= -2+18

3x=16

Divide by three on both sides.

$\frac{3x}{3}=\frac{16}{3}$

The answer is: $\frac{16}{3}$

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Algebra II : Solving Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #231 : Solving Equations

Example Question #232 : Solving Equations

Example Question #233 : Solving Equations

Example Question #234 : Solving Equations

Example Question #235 : Solving Equations

Example Question #236 : Solving Equations

Example Question #237 : Solving Equations

Example Question #238 : Solving Equations

Example Question #239 : Solving Equations

Example Question #231 : Solving Equations

All Algebra II Resources

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