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Algebra II : Algebra II

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Example Questions

Example Question #76 : Solving Inequalities

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

Possible Answers:

x>33

x<-21

x<-27

x>27

x<-33

Correct answer:

x<-27

Explanation:

Simplify the right side of the inequality.

-9x-3>-8x+24

Add on both sides of the inequality.

-9x-3+9x>-8x+24+9x

-3>x+24

Subtract 24 from both sides.

-3-24>x+24-24

Simplify both sides.

The answer is: x<-27

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Example Question #73 : Solving Inequalities

Solve the inequality: -10x(-2)>-2+31x

Possible Answers:

$x<-\frac{2}{19}$

$x<-\frac{2}{11}$

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

x>0

$x>-\frac{2}{19}$

Correct answer:

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

Explanation:

Be careful not to subtract or assume subtraction of the terms on the left side. The left side is a product of two values.

20x>-2+31x

Subtract 31x on both sides.

20x-31x>-2+31x-31x

The inequality becomes:

-11x>-2

Divide both sides by negative eleven. We will have to change the inequality sign.

$\frac{-11x}{-11}>\frac{-2}{-11}$

The answer is: $x<\frac{2}{11}$

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Example Question #311 : Basic Single Variable Algebra

Solve the following inequality: -3(-2x+7)<-2(5-6x)

Possible Answers:

$x<\frac{11}{18}$

$x>-\frac{11}{6}$

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

$x<\frac{31}{6}$

$x<\frac{31}{18}$

Correct answer:

$x>-\frac{11}{6}$

Explanation:

Use distribution to simplify both sides.

-3(-2x)+-3(7)<-2(5)-(-2)(6x)

Simplify all the terms in the inequality.

6x-21<-10+12x

Subtract on both sides. This will allow us to avoid changing the sign.

6x-21-6x<-10+12x-6x

-21< 6x-10

Add 10 on both sides.

-21+10< 6x-10+10

-11<6x

Divide by 6 on both sides.

$\frac{-11}{6}<\frac{6x}{6}$

$\frac{-11}{6}<x$

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

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Example Question #74 : Solving Inequalities

Solve the inequality: -8x-9>-36

Possible Answers:

$x<-\frac{45}{8}$

$x<\frac{27}{8}$

$x>-\frac{45}{8}$

$x>\frac{27}{8}$

$x<\frac{25}{4}$

Correct answer:

$x<\frac{27}{8}$

Explanation:

Add nine on both sides.

-8x-9+9>-36+9

-8x>-27

Divide by negative eight on both sides. We will need to switch the sign since we are dividing a negative value.

$\frac{-8x}{-8}<\frac{-27}{-8}$

The answer is: $x<\frac{27}{8}$

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Example Question #75 : Solving Inequalities

Solve the inequality: -4(-x+2)<6-4x

Possible Answers:

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

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

$\textup{No solution.}$

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

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

Correct answer:

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

Explanation:

Simplify the left side of the inequality by distribution.

-4(-x)+(-4)(2)<6-4x

4x-8<6-4x

Add on both sides.

4x-8+4x<6-4x+4x

The inequality becomes:

8x-8<6

Add 8 on both sides.

8x-8+8<6+8

8x<14

Divide by eight on both sides.

$\frac{8x}{8}<\frac{14}{8}$

Reduce the fractions.

The answer is: $x<\frac{7}{4}$

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Example Question #81 : Solving Inequalities

Solve the inequality: $3(-2x-7)\leq 8(-6x+2)$

Possible Answers:

$x\leq\frac{ 5}{42}$

$x\leq\frac{ 37}{42}$

$x\leq\frac{19}{42}$

$x\leq-\frac{ 5}{42}$

$x\leq\frac{ 5}{54}$

Correct answer:

$x\leq\frac{ 37}{42}$

Explanation:

Use distribution to simplify both sides.

$3(-2x)-(3)(7)\leq 8(-6x)+8(2)$

$-6x-21\leq -48x+16$

Add 48x on both sides.

$-6x-21+48x\leq -48x+16+48x$

Combine like terms.

$42x-21\leq 16$

Add 21 on both sides of the equation.

$42x-21+21\leq 16+21$

$42x\leq 37$

Divide by 42 on both sides.

$\frac{42x}{42}\leq\frac{ 37}{42}$

The answer is: $x\leq\frac{ 37}{42}$

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Example Question #82 : Solving Inequalities

Solve the inequalities: -3x+2<-41+6x

Possible Answers:

$x<\frac{43}{9}$

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

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

$x>\frac{43}{9}$

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

Correct answer:

$x>\frac{43}{9}$

Explanation:

Subtract from both sides.

-3x+2-6x<-41+6x-6x

Simplify both sides.

-9x+2<-41

Subtract two from both sides of the inequality.

-9x+2-2<-41-2

The inequality becomes:

-9x<-43

Divide by negative nine on both sides. Since we are dividing a negative value, we will need to switch the sign.

$\frac{-9x}{-9}>\frac{-43}{-9}$

The answer is: $x>\frac{43}{9}$

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Example Question #83 : Solving Inequalities

Solve the inequality: 5(x-19)>37

Possible Answers:

$x>\frac{132}{5}$

$x>\frac{204}{5}$

$x>-\frac{58}{5}$

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

$x>\frac{56}{5}$

Correct answer:

$x>\frac{132}{5}$

Explanation:

Distribute the five with the terms of the binomial.

5(x)-(5)(19)>37

Simplify both terms in parentheses.

5x-95>37

Add 95 on both sides of the inequality.

5x-95+95>37+95

5x>132

Divide by five on both sides.

$\frac{5x}{5}>\frac{132}{5}$

The answer is: $x>\frac{132}{5}$

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Example Question #84 : Solving Inequalities

Solve the inequality: 6-9x>7+10x

Possible Answers:

$x<\frac{13}{19}$

$x<-\frac{13}{19}$

$x<-\frac{1}{19}$

$x>-\frac{13}{19}$

$x>-\frac{1}{19}$

Correct answer:

$x<-\frac{1}{19}$

Explanation:

Add on both sides.

6-9x+9x>7+10x+9x

6>7+19x

Subtract seven from both sides.

6-7>7+19x-7

-1>19x

Divide by 19 on both sides.

$\frac{-1}{19}>\frac{19x}{19}$

Simplify both sides.

The answer is: $x<-\frac{1}{19}$

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Example Question #85 : Solving Inequalities

Solve the inequality: $-3x+4\leq 6-x$

Possible Answers:

$x\leq-5$

$x\geq-5$

$x\geq-1$

$x\leq-\frac{5}{2}$

$x\leq-1$

Correct answer:

$x\geq-1$

Explanation:

Add on both sides.

$-3x+4+3x\leq 6-x+3x$

$4\leq 6+2x$

Subtract six from both sides.

$4-6\leq 6+2x-6$

Simplify both sides.

$-2\leq2x$

Divide by two on both sides. We do not need to change the sign since we are dividing by a positive coefficient.

$\frac{-2}{2}\leq\frac{2x}{2}$

$-1\leq x$

The answer is: $x\geq-1$

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #76 : Solving Inequalities

Example Question #73 : Solving Inequalities

Example Question #311 : Basic Single Variable Algebra

Example Question #74 : Solving Inequalities

Example Question #75 : Solving Inequalities

Example Question #81 : Solving Inequalities

Example Question #82 : Solving Inequalities

Example Question #83 : Solving Inequalities

Example Question #84 : Solving Inequalities

Example Question #85 : Solving Inequalities

All Algebra II Resources

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