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Algebra II : Solving Inequalities

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Example Questions

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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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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Algebra II : Solving Inequalities

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #71 : Solving Inequalities

Example Question #71 : Solving Inequalities

Example Question #72 : Solving Inequalities

Example Question #111 : Inequalities

Example Question #71 : Solving Inequalities

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

All Algebra II Resources

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