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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #66 : Solving Inequalities

Solve the inequality: -3x+26>14-7x

Possible Answers:

x<-3

x>-3

x>-4

x>3

x<-4

Correct answer:

x>-3

Explanation:

Add on both sides.

-3x+26+(7x)>14-7x+(7x)

Simplify both sides of the inequality.

4x+26>14

Subtract 26 on both sides.

4x+26-26>14-26

Simplify.

4x>-12

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

$\frac{4x}{4}>\frac{-12}{4}$

The answer is: x>-3

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Example Question #67 : Solving Inequalities

Solve the inequality: 9(-3x+2)>8(2-3x)

Possible Answers:

$x>\frac{2}{3}$

$x<-\frac{2}{3}$

$x<\frac{2}{3}$

$x<-\frac{34}{3}$

$x<\frac{34}{3}$

Correct answer:

$x<\frac{2}{3}$

Explanation:

Use the distributive property to simplify both the left and right sides of the inequality.

9(-3x+2)>8(2-3x)

-27x+18>16-24x

Add 27x on both sides.

-27x+18+27x>16-24x+27x

18>16+3x

Subtract 16 from both sides.

18-16>16+3x-16

2>3x

Divide by three on both sides.

$\frac{2}{3}>\frac{3x}{3}$

$\frac{2}{3}>x$

The answer is: $x<\frac{2}{3}$

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Example Question #68 : Solving Inequalities

Solve: 2x-3>7x-9

Possible Answers:

$x<\frac{5}{6}$

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

$x<\frac{6}{5}$

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

$x>\frac{6}{5}$

Correct answer:

$x<\frac{6}{5}$

Explanation:

Subtract from both sides.

2x-3-2x>7x-9-2x

-3>5x-9

Add 9 on both sides.

-3+9>5x-9+9

Simplify both sides.

6>5x

Divide both sides by five.

$\frac{6}{5}>\frac{5x}{5}$

$\frac{6}{5}>x$

The answer is: $x<\frac{6}{5}$

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Example Question #69 : Solving Inequalities

Solve: 8(9x-4)>-56

Possible Answers:

x>3

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

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

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

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

Correct answer:

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

Explanation:

Divide by 8 on both sides.

$\frac{8(9x-4)}{8}>\frac{-56}{8}$

Simplify both sides.

9x-4>-7

Add four on both sides.

9x-4+4>-7+4

9x>-3

Divide by nine on both sides.

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

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

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Example Question #70 : Solving Inequalities

Simplify the inequality: 9x+8>10x-6

Possible Answers:

x<14

x<-14

$x<\frac{14}{19}$

x>14

$x<-\frac{14}{19}$

Correct answer:

x<14

Explanation:

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

To avoid dividing a negative coefficient and changing the sign, we can subtract on both sides.

9x+8-9x>10x-6-9x

Simplify the inequality.

8>x-6

Add 6 on both sides.

8+6>x-6+6

14>x

The answer is: x<14

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Example Question #71 : Solving Inequalities

Simplify the inequality: -2(3x-1)>-3(4-x)

Possible Answers:

$x<-\frac{14}{9}$

$x<\frac{14}{9}$

$x<-\frac{10}{9}$

$x>-\frac{7}{9}$

$x>-\frac{14}{9}$

Correct answer:

$x<\frac{14}{9}$

Explanation:

Distribute the negative numbers through the binomials.

-2(3x)-(-2)(1)>-3(4)-(-3)(x)

Simplify the terms.

-6x+2>-12+3x

Add on both sides.

-6x+2+6x>-12+3x+6x

2>-12+9x

Add 12 on both sides.

14>9x

Divide by 9 on both sides.

$\frac{14}{9}>\frac{9x}{9}$

The answer is: $x<\frac{14}{9}$

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Example Question #71 : Solving Inequalities

Solve the inequality: $\frac{1}{3}x-3>12$

Possible Answers:

x<4

x>45

x<45

x<3

x>3

Correct answer:

x>45

Explanation:

Add three on both sides.

$\frac{1}{3}x-3+3>12+3$

The inequality becomes:

$\frac{1}{3}x>15$

Multiply by three on both sides.

$\frac{1}{3}x\cdot 3>15\cdot 3$

The answer is: x>45

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Example Question #72 : Solving Inequalities

Solve the inequality: 9x-18>56

Possible Answers:

$x>\frac{74}{9}$

$x<\frac{74}{9}$

$x>\frac{23}{3}$

$x<\frac{48}{9}$

$x>\frac{38}{9}$

Correct answer:

$x>\frac{74}{9}$

Explanation:

Add 18 on both sides.

9x-18+18>56+18

Simplify both sides.

9x>74

Divide by nine on both sides.

$\frac{9x}{9}>\frac{74}{9}$

The answer is: $x>\frac{74}{9}$

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Example Question #111 : Inequalities

Solve the inequality: $8x\leq -9x+7$

Possible Answers:

$x\geq\frac{7}{17}$

$x\geq7$

$x\leq\frac{7}{17}$

$x\leq7$

$x\leq-7$

Correct answer:

$x\leq\frac{7}{17}$

Explanation:

Add on both sides of the inequality.

$8x+9x\leq -9x+7+9x$

The inequality becomes:

$17x\leq7$

Divide by seventeen on both sides.

$\frac{17x}{17}\leq\frac{7}{17}$

The answer is: $x\leq\frac{7}{17}$

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Example Question #71 : Solving Inequalities

Solve the inequality: $-\frac{1}{4}x+6\leq 10$

Possible Answers:

$x\leq-16$

$x\leq-1$

$x\leq-64$

$x\geq-1$

$x\geq-16$

Correct answer:

$x\geq-16$

Explanation:

Subtract six from both sides.

$-\frac{1}{4}x+6-6\leq 10-6$

$-\frac{1}{4}x\leq4$

Multiply by negative four on both sides. Note that since this is similar to divide by a negative value, we will have to change the direction of the sign.

$-\frac{1}{4}x \cdot -4\geq4 \cdot-4$

The answer is: $x\geq-16$

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #66 : Solving Inequalities

Example Question #67 : Solving Inequalities

Example Question #68 : Solving Inequalities

Example Question #69 : Solving Inequalities

Example Question #70 : Solving Inequalities

Example Question #71 : Solving Inequalities

Example Question #71 : Solving Inequalities

Example Question #72 : Solving Inequalities

Example Question #111 : Inequalities

Example Question #71 : Solving Inequalities

All Algebra II Resources

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