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Algebra II : Solving Inequalities

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #2114 : Algebra Ii

Solve:

$-\frac{x-1}{5}<7$

Possible Answers:

$x\geq-34$

x<-34

$x\leq-34$

x>34

x>-34

Correct answer:

x>-34

Explanation:

To solve, we must first multiply each side by -1. Multiplying (or dividing) by the negative flips the inequality sign:

$\frac{x-1}{5}>-7$

Now, we isolate x by multiplying by 5 and adding 1 to both sides:

x-1>-35

x>-34

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Example Question #2115 : Algebra Ii

Solve the inequality: 2z-9>54

Possible Answers:

$z<\frac{45}{2}$

$z<\frac{63}{2}$

z>28

$z>\frac{63}{2}$

$z>\frac{45}{2}$

Correct answer:

$z>\frac{63}{2}$

Explanation:

Add nine on both sides.

2z-9+9>54+9

Simplify both sides.

2z>63

Divide by two on both sides.

$\frac{2z}{2}>\frac{63}{2}$

It is not necessary to change the sign.

The answer is: $z>\frac{63}{2}$

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Example Question #2116 : Algebra Ii

Solve the inequality: $-3x+4\geq 35$

Possible Answers:

$x\geq -\frac{31}{3}$

$x\leq -\frac{31}{3}$

$x\geq -13$

$x\leq -13$

$x> -\frac{31}{3}$

Correct answer:

$x\leq -\frac{31}{3}$

Explanation:

Subtract 4 from both sides of the equation.

$-3x+4-4\geq 35-4$

Simplify both sides.

$-3x\geq 31$

Divide both sides by negative three. Since we are dividing by a negative number, we will need to switch the direction of the sign.

$\frac{-3x}{-3}\leq \frac{31}{-3}$

The answer is: $x\leq -\frac{31}{3}$

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Example Question #2117 : Algebra Ii

Solve the inequality: -8x-3>9

Possible Answers:

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

x<20

x>20

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

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

Correct answer:

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

Explanation:

Add three on both sides.

-8x-3+3>9+3

Simplify both sides.

-8x>12

Divide by negative eight on both sides. Since we are dividing by a negative sign, the inequality sign will switch directions.

$\frac{-8x}{-8}<\frac{12}{-8}$

Reduce both fractions.

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

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Example Question #2118 : Algebra Ii

Solve: -6x+5>18

Possible Answers:

$x<-\frac{13}{6}$

$x>-\frac{13}{6}$

$x\leq-\frac{23}{6}$

$x>-\frac{23}{6}$

$x<-\frac{23}{6}$

Correct answer:

$x<-\frac{13}{6}$

Explanation:

In order to isolate the x-variable, first subtract five from both sides.

-6x+5-5>18-5

Simplify both sides.

-6x>13

Divide by negative six on both sides. Remember to switch the sign since we are dividing by a negative number.

$\frac{-6x}{-6}>\frac{13}{-6}$

The answer is: $x<-\frac{13}{6}$

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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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Algebra II : Solving Inequalities

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #2114 : Algebra Ii

Example Question #2115 : Algebra Ii

Example Question #2116 : Algebra Ii

Example Question #2117 : Algebra Ii

Example Question #2118 : Algebra Ii

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

All Algebra II Resources

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