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Algebra II : Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #201 : Solving Equations

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

Possible Answers:

$-\frac{1}{9}$

$\textup{No solution.}$

$-\frac{1}{2}$

$-\frac{1}{3}$

$-\frac{1}{6}$

Correct answer:

$-\frac{1}{6}$

Explanation:

Group like terms. Start with the x-variable.

Add on both sides.

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

18x-3=-6

Add three on both sides.

18x-3+3=-6+3

Simplify both sides.

18x=-3

Divide by 18 on both sides.

$\frac{18x}{18}=\frac{-3}{18}$

Simplify both fractions.

$x=-\frac{1}{6}$

The answer is: $-\frac{1}{6}$

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Example Question #211 : Solving Equations

Solve the equation: -3x+10 = -3

Possible Answers:

$-\frac{7}{3}$

$\frac{7}{3}$

$-\frac{13}{3}$

$\frac{13}{3}$

Correct answer:

$\frac{13}{3}$

Explanation:

Subtract ten from both sides.

-3x+10 -10= -3-10

Simplify both sides.

-3x=-13

Divide by negative three on both sides.

$\frac{-3x}{-3}=\frac{-13}{-3}$

Simplify both fractions on each side of the equation.

The answer is: $x=\frac{13}{3}$

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Example Question #211 : Solving Equations

Solve for

$\frac{5y^3+4^5}{23*8^4}=2^5$

Possible Answers:

$y\approx 37.51$

$y\approx 39.85$

$y\approx 44.49$

$y\approx 84.47$

None of these

Correct answer:

$y\approx 84.47$

Explanation:

$y^3=\frac{(2^5)(23*8^4)-4^5}{5}$

5y^3+4^5=(2^5)(23*8^4)

5y^3=(2^5)(23*8^4)-4^5

$y^3=\frac{(2^5)(23*8^4)-4^5}{5}$

$y=\sqrt[3]{\frac{(2^5)(23*8^4)-4^5}{5}}$

$y=\sqrt[3]{\frac{(32)(23*4096)-1024}{5}}$

$y=\sqrt[3]{\frac{(32)(94208)-1024}{5}}$

$y=\sqrt[3]{\frac{3014656-1024}{5}}$

$y=\sqrt[3]{\frac{3013632}{5}}$

$y=\sqrt[3]{602726.4}$

$y\approx 84.47$

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Example Question #342 : Equations

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

Possible Answers:

$\frac{2}{3}$

$\textup{There is no solution.}$

$-\frac{2}{3}$

Correct answer:

Explanation:

Solve by grouping the variables and the integers on separate sides.

Add on both sides.

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

12x+3=-9

Subtract three on both sides.

12x+3-3=-9-3

12x=-12

Divide by 12 on both sides.

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

Reduce both fractions.

The answer is:

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Example Question #214 : Solving Equations

Solve the equation: $\frac{3}{8}x-\frac{11}{8}=\frac{1}{8}$

Possible Answers:

$-\frac{1}{4}$

$\frac{1}{4}$

$-\frac{1}{8}$

Correct answer:

Explanation:

The fractions all have a common denominator on both sides.

Multiply by eight on both sides of the equation.

$8(\frac{3}{8}x-\frac{11}{8})=8(\frac{1}{8})$

The equation becomes:

3x-11=1

Add 11 on both sides.

3x-11+11=1+11

3x=12

Divide by 3 on both sides.

The answer is: x=4

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Example Question #215 : Solving Equations

Solve the equation: 3x+62 = -47

Possible Answers:

$-\frac{109}{3}$

$-\frac{1}{5}$

$\frac{109}{3}$

$-\frac{25}{3}$

Correct answer:

$-\frac{109}{3}$

Explanation:

Subtract 62 from both sides of the equation.

3x+62-62 = -47-62

Simplify both sides.

3x=-109

Divide by three on both sides.

$\frac{3x}{3}=\frac{-109}{3}$

The right side is irreducible.

The answer is: $x=-\frac{109}{3}$

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Example Question #216 : Solving Equations

Solve the equation: 4x-9 = 8+12x

Possible Answers:

$-\frac{17}{8}$

$-\frac{7}{8}$

$-\frac{16}{17}$

$-\frac{31}{8}$

$-\frac{1}{8}$

Correct answer:

$-\frac{17}{8}$

Explanation:

Isolate the terms with the x-variable on one side, and the integers on the other.

Subtract on both sides.

4x-9 -4x = 8+12x-4x

-9=8x+8

Subtract 8 from both sides.

-9-8=8x+8-8

-17=8x

Divide by eight on both sides.

$\frac{-17}{8}=\frac{8x}{8}$

The answer is: $-\frac{17}{8}$

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Example Question #341 : Equations

Solve the equation: 9x+7 = 2(x-2)

Possible Answers:

$\frac{3}{7}$

$-\frac{11}{7}$

$-\frac{22}{7}$

$-\frac{9}{7}$

$-\frac{22}{3}$

Correct answer:

$-\frac{11}{7}$

Explanation:

Simplify by first distributing the two through the binomial on the right side of the equation.

9x+7 = 2x-4

Subtract both sides by .

9x+7-2x = 2x-4-2x

Simplify both sides.

7x+7 = -4

Subtract seven on both sides.

7x+7 -7= -4-7

7x=-11

Divide by seven on both sides.

The answer is: $x=-\frac{11}{7}$

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Example Question #218 : Solving Equations

Solve the equation: 9x-3=4x+8

Possible Answers:

$-\frac{11}{13}$

$\frac{11}{5}$

$-\frac{11}{5}$

$\frac{11}{13}$

$-\frac{5}{13}$

Correct answer:

$\frac{11}{5}$

Explanation:

Subtract the term on both sides of the equation.

9x-3-(4x)=4x+8-(4x)

Simplify the equation.

5x-3 =8

Add three on both sides.

5x-3 +(3)=8+(3)

5x=11

Divide by five on both side

$\frac{5x}{5}= \frac{11}{5}$

The answer is: $\frac{11}{5}$

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Example Question #343 : Equations

Solve for .

5(x+4)=20

Possible Answers:

Correct answer:

Explanation:

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

5(x+4)=20 Divide on both sides.

x+4=4 Subtract on both sides.

x=0

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Algebra II : Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #201 : Solving Equations

Example Question #211 : Solving Equations

Example Question #211 : Solving Equations

Example Question #342 : Equations

Example Question #214 : Solving Equations

Example Question #215 : Solving Equations

Example Question #216 : Solving Equations

Example Question #341 : Equations

Example Question #218 : Solving Equations

Example Question #343 : Equations

All Algebra II Resources

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