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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #41 : Solving Inequalities

Solve the inequality: $-2x+3\geq 9x-7$

Possible Answers:

$x\geq \frac{11}{10}$

$x\leq \frac{10}{11}$

$x\geq -\frac{10}{7}$

$x\geq \frac{4}{7}$

$x\geq \frac{10}{11}$

Correct answer:

$x\leq \frac{10}{11}$

Explanation:

Add on both sides.

$-2x+3+(2x)\geq 9x-7+(2x)$

$3\geq11x-7$

Add seven on both sides.

$3+(7)\geq11x-7+(7)$

$10\geq11x$

Divide by 11 on both sides.

$\frac{10}{11}\geq \frac{11x}{11}$

$\frac{10}{11}\geq x$ OR $x\leq \frac{10}{11}$

The answer is: $x\leq \frac{10}{11}$

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Example Question #42 : Solving Inequalities

Solve the inequality: x-3>6x-4

Possible Answers:

$x>-\frac{1}{5}$

$x<\frac{1}{5}$

$x>\frac{1}{5}$

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

$x<-\frac{1}{5}$

Correct answer:

$x<\frac{1}{5}$

Explanation:

To solve the inequality, isolate the integers on one side of the inequality, and the x-variables on another side.

To avoid having to divide by a negative coefficient of , subtract on both sides.

x-3-(x)>6x-4-(x)

-3>5x-4

Add four on both sides.

-3+4>5x-4+4

Simplify both sides.

1>5x

Divide by 5 on both sides.

$\frac{1}{5}>\frac{5x}{5}$

$\frac{1}{5}>x$

The answer is: $x<\frac{1}{5}$

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Example Question #43 : Solving Inequalities

Solve the inequality: 8x-9>72

Possible Answers:

$x<\frac{81}{8}$

x>1

$x>\frac{81}{8}$

$x<\frac{63}{8}$

$x>\frac{63}{8}$

Correct answer:

$x>\frac{81}{8}$

Explanation:

Add nine on both sides.

8x-9+9>72+9

Simplify both sides.

8x>81

Divide by eight on both sides. There is no need to switch the sign.

$\frac{8x}{8}>\frac{81}{8}$

The answer is: $x>\frac{81}{8}$

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Example Question #44 : Solving Inequalities

Solve the inequality: -3x+6<-6x+7

Possible Answers:

$x<\frac{13}{3}$

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

$x<-\frac{1}{3}$

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

$x<\frac{1}{3}$

Correct answer:

$x<\frac{1}{3}$

Explanation:

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

Add on both sides of the inequality.

-3x+6+(6x)<-6x+7+(6x)

3x+6<7

Subtract six from both sides.

3x+6-6<7-6

3x<1

Divide by three on both sides and simplify.

The answer is: $x<\frac{1}{3}$

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Example Question #45 : Solving Inequalities

Solve the inequality: $6x-3\leq 9x+6$

Possible Answers:

$x\leq-1$

$x\leq-3$

$x\geq3$

$x\geq-1$

$x\geq-3$

Correct answer:

$x\geq-3$

Explanation:

In order to isolate the variable, subtract from both sides. This will prevent us from dividing a negative coefficient and change the sign.

$6x-3-6x\leq 9x+6-6x$

Simplify both sides.

$-3\leq 3x+6$

Subtract six on both sides.

$-3-6\leq 3x+6-6$

Simplify both sides.

$-9\leq 3x$

Divide by three on both sides.

$\frac{-9}{3}\leq\frac{ 3x}{3}$

Simplify both sides.

The answer is: $x\geq-3$

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Example Question #51 : Solving Inequalities

Solve the inequality: 4(x-2)>8(2x-3)

Possible Answers:

$x<\frac{3}{4}$

$x<\frac{4}{3}$

$x<-\frac{4}{3}$

$x<-\frac{8}{3}$

$x<\frac{8}{3}$

Correct answer:

$x<\frac{4}{3}$

Explanation:

Use the distributive property to simplify both sides of the inequality.

4x-8>16x-24

Subtract on both sides.

4x-8-4x>16x-24-4x

The inequality becomes:

-8>12x-24

Add 24 on both sides.

-8+24>12x-24+24

Simplify both sides.

16>12x

Divide by 12 on both sides.

$\frac{16}{12}>\frac{12x}{12}$

$\frac{4}{3}>x$

The answer is: $x<\frac{4}{3}$

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Example Question #52 : Solving Inequalities

Solve the inequality: $3x\leq6(6x-3)$

Possible Answers:

$x\leq9$

$x\leq \frac{6}{11}$

$x\geq \frac{2}{11}$

$x\geq \frac{6}{11}$

$x\leq-\frac{9}{11}$

Correct answer:

$x\geq \frac{6}{11}$

Explanation:

In order to solve for x, we will first need to simplify the right side.

Multiply the six through both terms of the binomial.

$3x\leq36x-18$

Subtract 36x from both sides.

$3x-36x\leq36x-18-36x$

$-33x\leq -18$

Divide by negative 33 on both sides. This will require a sign change.

$\frac{-33x}{-33}\geq \frac{-18}{-33}$

$x\geq\frac{-3\times 6}{-3\times 11}$

The answer is: $x\geq \frac{6}{11}$

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Example Question #53 : Solving Inequalities

Solve the inequality: 4(x-3)> 6(9x-3)

Possible Answers:

$x<\frac{3}{5}$

$x<\frac{3}{25}$

$x<-\frac{3}{5}$

$x>-\frac{3}{25}$

$x<\frac{25}{3}$

Correct answer:

$x<\frac{3}{25}$

Explanation:

Use the distributive property to expand both sides.

4(x-3)> 6(9x-3)

4x-12>54x-18

Subtract on both sides.

4x-12-4x>54x-18-4x

-12>50x-18

Add 18 on both sides.

-12+18>50x-18+18

The inequality becomes:

6>50x

Divide by 50 on both sides.

$\frac{6}{50}>\frac{50x}{50}$

The answer is: $x<\frac{3}{25}$

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Example Question #51 : Solving Inequalities

Solve the inequality: 8x-3> 29

Possible Answers:

$x<-\frac{13}{4}$

x>4

$x>\frac{13}{4}$

x<-4

x>-4

Correct answer:

x>4

Explanation:

Add three on both sides.

8x-3+3> 29+3

Simplify both sides.

8x>32

Divide by 8 on both sides.

$\frac{8x}{8}>\frac{32}{8}$

Simplify both sides.

The answer is: x>4

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Example Question #55 : Solving Inequalities

Solve the inequality: $3+x\leq 6-8x$

Possible Answers:

$x\leq \frac{1}{3}$

$x\leq 1$

$x\leq 3$

$x\leq -1$

$x\leq -\frac{1}{3}$

Correct answer:

$x\leq \frac{1}{3}$

Explanation:

Add on both sides of the inequality.

$3+x+(8x)\leq 6-8x+(8x)$

Simplify both sides.

$9x+3\leq6$

Subtract three from both sides.

$9x+3-3\leq6-3$

$9x\leq3$

Divide by nine on both sides.

$\frac{9x}{9}\leq\frac{3}{9}$

Simplify both fractions.

The answer is: $x\leq \frac{1}{3}$

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #41 : Solving Inequalities

Example Question #42 : Solving Inequalities

Example Question #43 : Solving Inequalities

Example Question #44 : Solving Inequalities

Example Question #45 : Solving Inequalities

Example Question #51 : Solving Inequalities

Example Question #52 : Solving Inequalities

Example Question #53 : Solving Inequalities

Example Question #51 : Solving Inequalities

Example Question #55 : Solving Inequalities

All Algebra II Resources

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