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Algebra II : Solving Inequalities

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Example Question #285 : Basic Single Variable Algebra

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

Possible Answers:

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

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

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

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

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

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 #286 : Basic Single Variable Algebra

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

Possible Answers:

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

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

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

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

$x\leq9$

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 #281 : Basic Single Variable Algebra

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

Possible Answers:

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

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

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

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

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

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>-4

x<-4

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

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 #289 : Basic Single Variable Algebra

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

Possible Answers:

$x\leq 3$

$x\leq 1$

$x\leq -1$

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

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

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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Example Question #52 : Solving Inequalities

Solve the inequality: $-8x+40\geq -5x-20$

Possible Answers:

$x\leq \frac{20}{3}$

$x\leq 20$

$x\leq -\frac{20}{13}$

$x\leq -20$

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

Correct answer:

$x\leq 20$

Explanation:

Add on both sides of the inequality.

$-8x+40+(8x)\geq -5x-20+(8x)$

Simplify both sides.

$40\geq 3x-20$

Add 20 on both sides.

$40+20\geq 3x-20+20$

$60\geq3x$

Divide by three on both sides.

$\frac{60}{3}\geq\frac{3x}{3}$

$20\geq x$

The answer is: $x\leq 20$

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Example Question #51 : Solving Inequalities

Solve the inequality: $5x-8\geq -82$

Possible Answers:

$x\leq-\frac{74}{5}$

$x\leq-18$

x<-18

$x\geq-\frac{74}{5}$

$x\geq-18$

Correct answer:

$x\geq-\frac{74}{5}$

Explanation:

Add 8 on both sides.

$5x-8+8\geq -82+8$

$5x\geq -74$

Divide by five on both sides. It is not necessary to switch the direction of the sign.

$\frac{5x}{5}\geq \frac{-74}{5}$

Simplify both sides.

The answer is: $x\geq-\frac{74}{5}$

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Example Question #52 : Solving Inequalities

Solve the inequality: 6x-9>81-3x

Possible Answers:

x>-30

x>10

x>-18

x<-18

x>30

Correct answer:

x>10

Explanation:

Add on both sides.

6x-9+3x>81-3x+3x

9x-9>81

Add nine on both sides.

9x-9+9>81+9

9x>90

Divide by nine on both sides.

$\frac{9x}{9}>\frac{90}{9}$

The answer is: x>10

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Example Question #53 : Solving Inequalities

Solve the inequality: -5x+3>-6x+18

Possible Answers:

x>15

x<15

$x<-\frac{15}{11}$

$x>-\frac{15}{11}$

$x>-\frac{11}{15}$

Correct answer:

x>15

Explanation:

Add on both sides.

-5x+3+6x>-6x+18+6x

Simplify both sides.

x+3>18

Subtract 3 on both sides.

x+3-3>18-3

The answer is: x>15

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Example Question #54 : Solving Inequalities

Solve the inequality: -3(x-6)>-15

Possible Answers:

x>11

x>-1

x<-1

x<11

x<-11

Correct answer:

x<11

Explanation:

Divide by negative three on both sides. This operation will require changing the signs.

$\frac{-3(x-6)}{-3}>\frac{-15}{-3}$

x-6<5

Add 6 on both sides.

x-6+6<5+6

The answer is: x<11

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Algebra II : Solving Inequalities

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #285 : Basic Single Variable Algebra

Example Question #286 : Basic Single Variable Algebra

Example Question #281 : Basic Single Variable Algebra

Example Question #51 : Solving Inequalities

Example Question #289 : Basic Single Variable Algebra

Example Question #52 : Solving Inequalities

Example Question #51 : Solving Inequalities

Example Question #52 : Solving Inequalities

Example Question #53 : Solving Inequalities

Example Question #54 : Solving Inequalities

All Algebra II Resources

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