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Algebra II : Basic Single-Variable Algebra

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #412 : Equations

Solve the equation: 9-4x= 11-9x

Possible Answers:

$\frac{20}{13}$

$\frac{2}{13}$

$-\frac{2}{13}$

$\frac{2}{5}$

Correct answer:

$\frac{2}{5}$

Explanation:

Add on both sides.

9-4x+9x= 11-9x+9x

Combine like-terms on both sides.

9+5x =11

Subtract nine from both sides.

9+5x -9=11-9

5x=2

Divide by five on both sides.

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

The answer is: $\frac{2}{5}$

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Example Question #413 : Equations

Solve the equation: 8x-7 = 2x+7

Possible Answers:

$\frac{7}{3}$

$\frac{3}{8}$

$-\frac{7}{3}$

$\frac{14}3$

Correct answer:

$\frac{7}{3}$

Explanation:

Subtract from both sides.

8x-7-2x = 2x+7-2x

The equation becomes:

6x-7=7

Add seven on both sides.

6x-7+7=7+7

6x=14

Divide by six on both sides and reduce the fraction.

$\frac{6x}{6}=\frac{14}{6}$

The answer is: $\frac{7}{3}$

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Example Question #414 : Equations

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

Possible Answers:

$\frac{4}{13}$

$-\frac{4}{13}$

$\frac{5}{13}$

$\frac{18}{13}$

$\frac{20}{13}$

Correct answer:

$\frac{20}{13}$

Explanation:

Add 12 on both sides.

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

9x= -4x+20

Add on both sides of the equation.

9x+4x= -4x+20+4x

Simplify both sides.

13x = 20

Divide by 13 on both sides.

$\frac{13x }{13}= \frac{20}{13}$

The answer is: $\frac{20}{13}$

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Example Question #2601 : Algebra Ii

Solve the equation: 8x-9 = 31-8x

Possible Answers:

$-\frac{5}{2}$

$\textup{No solution.}$

$\frac{5}{2}$

$\frac{11}{8}$

$-\frac{11}{8}$

Correct answer:

$\frac{5}{2}$

Explanation:

Add on both sides.

8x-9 +8x= 31-8x+8x

The equation becomes:

16x-9 = 31

Add nine on both sides.

16x-9+9 = 31+9

The equation becomes:

16x = 40

Divide by 16 on both sides.

$\frac{16x }{16}= \frac{40}{16}$

Reduce the fractions.

$\frac{40}{16} = \frac{8\times 5}{8\times 2}$

The answer is: $\frac{5}{2}$

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Example Question #761 : Basic Single Variable Algebra

Solve the equation: $\frac{1}{3}x-\frac{1}{4}=\frac{3}{7}$

Possible Answers:

$\frac{47}{28}$

$-\frac{47}{28}$

$\frac{31}{28}$

$\frac{57}{28}$

$-\frac{15}{28}$

Correct answer:

$\frac{57}{28}$

Explanation:

Determine the least common denominator of the fractions by multiplying all the denominators together.

3(4)(7)= 84

We can multiply both sides by 84 in order to eliminate the fractions.

$84(\frac{1}{3}x-\frac{1}{4})=\frac{3}{7}\cdot 84$

Simplify both sides.

$28x -21 = 3\cdot 12$

28x -21 = 36

Add 21 on both sides.

28x = 57

Divide by 28 on both sides.

$\frac{28x }{28}= \frac{57}{28}$

The answer is: $\frac{57}{28}$

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Example Question #761 : Basic Single Variable Algebra

$f(x)=\frac{1}{3}x+4$

and

g(x)=3x+4 ,

what is the value of g(f(6)) ?

Possible Answers:

Correct answer:

Explanation:

In order to answer this question, you must first find f(6) .

Plugging in 6 for x in the f(x) equation,

$\\f(x)=\frac{1}{3}x+4 \\ \\f(6)=\frac{1}{3}(6)+4 \\ \\f(6)=\frac{2\cdot 3}{3}+4 \\ \\f(6)=2+4 \\ \\f(6)=6$

you get 6 as your answer, so then you plug 6 in as the x in the g(x) equation.

$\\g(x)=3x+4 \\g(6)=3(6)+4 \\g(6)=18+4 \\g(6)=22$ .

Thus g(f(6))=22 .

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Example Question #412 : Equations

Solve 4x-2x=4 for .

Possible Answers:

x=2

x=0

x= -2

x=3

x=1

Correct answer:

x=2

Explanation:

4x-2x=2x , then setting 2x=4 and dividing the entire equation by , you get x=2 .

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Example Question #413 : Equations

4x+2x=?

Possible Answers:

$6x^{2}$

Correct answer:

Explanation:

When adding 4x+2x , you only add the coefficients and keep the variable, so 4+2=6 and then keep the , so it equals .

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Example Question #281 : Solving Equations

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

Possible Answers:

$\frac{4}{17}$

$\frac{13}{17}$

$-\frac{4}{17}$

Correct answer:

$-\frac{4}{17}$

Explanation:

Isolate the x-variable by subtracting on both sides.

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

Simplify both sides.

-17x = 4

Divide by negative 17 on both sides.

$\frac{-17x}{-17} =\frac{4 }{-17}$

The answer is: $-\frac{4}{17}$

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Example Question #282 : Solving Equations

Solve the equation: 2x-6 = 9x-7

Possible Answers:

$-\frac{13}{7}$

$\frac{1}{7}$

$\frac{13}{7}$

$\frac{13}{11}$

$\frac{11}{3}$

Correct answer:

$\frac{1}{7}$

Explanation:

Subtract from both sides of the equation.

2x-6 -2x= 9x-7-2x

-6 =7x-7

Add seven on both sides.

-6 +7=7x-7+7

1=7x

Divide by 7 on both sides.

$\frac{1}{7}=\frac{7x}{7}$

The answer is: $\frac{1}{7}$

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Algebra II : Basic Single-Variable Algebra

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #412 : Equations

Example Question #413 : Equations

Example Question #414 : Equations

Example Question #2601 : Algebra Ii

Example Question #761 : Basic Single Variable Algebra

Example Question #761 : Basic Single Variable Algebra

Example Question #412 : Equations

Example Question #413 : Equations

Example Question #281 : Solving Equations

Example Question #282 : Solving Equations

All Algebra II Resources

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