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Algebra 1 : Systems of Inequalities

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Example Questions

Example Question #2234 : Algebra 1

Solve the inequaltiy: -9x<99

Possible Answers:

x<-108

x>-108

x>11

x>-11

x<-11

Correct answer:

x>-11

Explanation:

Divide both sides by negative nine. When we divide by a negative sign, be sure to switch the sign.

$-\frac{9x}{-9}<\frac{99}{-9}$

Simplify both sides.

The answer is: x>-11

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Example Question #27 : How To Find The Solution To An Inequality With Division

Solve: -3x+3 >-12

Possible Answers:

x>5

x>-5

$x\geq-5$

x<-5

x<5

Correct answer:

x<5

Explanation:

We will need to isolate the term with the x variable.

First subtract three from both sides.

-3x+3 -(3)>-12-(3)

Simplify both sides of the inequality.

-3x>-15

Divide by a negative three on both sides. This will change switch the sign.

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

Simplify both sides.

The answer is: x<5

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Example Question #111 : Equations / Inequalities

Find the solution: -6x<52

Possible Answers:

$x>-\frac{26}{3}$

x<-9

$x\leq-\frac{26}{3}$

$x\geq-\frac{26}{3}$

$x<-\frac{26}{3}$

Correct answer:

$x>-\frac{26}{3}$

Explanation:

Divide by negative six on both sides of the inequality.

$\frac{-6x}{-6}<\frac{52}{-6}$

Simplify both sides. When dividing by a negative, the sign will switch.

$x>-\frac{52}{6}$

Rewrite the numerator and denominator with common factors.

$x>-\frac{2\times 26}{2\times 3}$

Cancel the two on the numerator and denominator.

The answer is: $x>-\frac{26}{3}$

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Example Question #29 : How To Find The Solution To An Inequality With Division

Solve the inequality: $-9y>-\frac{1}{3}$

Possible Answers:

y<3

$y>\frac{1}{27}$

$y\leq\frac{1}{27}$

y>3

$y<\frac{1}{27}$

Correct answer:

$y<\frac{1}{27}$

Explanation:

In order to isolate the y variable, divide by negative nine on both sides. When dividing by a negative sign, the sign will switch directions.

$\frac{-9y}{-9}>\frac{-\frac{1}{3}}{-9}$

Simplify both sides. When dividing by a negative nine, we can rewrite that as multiplying by negative one-ninth.

$y<-\frac{1}{3} \cdot \frac{1}{-9}$

Simplify the right side.

The answer is: $y<\frac{1}{27}$

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Example Question #2241 : Algebra 1

Solve the inequality: $3x>\frac{1}{4}$

Possible Answers:

$x>\frac{1}{12}$

x>12

$x\leq \frac{1}{12}$

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

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

Correct answer:

$x>\frac{1}{12}$

Explanation:

Divide by three on both sides.

$\frac{3x}{3}>\frac{\frac{1}{4}}{3}$

Reduce both sides. For the right side, dividing by three is similar to multiplying by one-third.

$x>\frac{1}{4} \times \frac{1}{3}$

Simplify.

The answer is: $x>\frac{1}{12}$

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Example Question #31 : How To Find The Solution To An Inequality With Division

Find the solution of the inequality: $-4x<\frac{3}{4}$

Possible Answers:

$x>-\frac{16}{3}$

$x>-\frac{3}{16}$

x>-3

x<-3

$x<-\frac{3}{16}$

Correct answer:

$x>-\frac{3}{16}$

Explanation:

To isolate the x-variable, we will need to divide by negative four on both sides. This is the same as multiplying negative one fourth on both sides.

Since we have a negative in front, we will also need to switch the sign.

$-4x\cdot -\frac{1}{4}<\frac{3}{4}\cdot -\frac{1}{4}$

Simplify both sides of the equation and switch the sign.

$x>-\frac{3}{16}$

The answer is: $x>-\frac{3}{16}$

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Example Question #111 : Systems Of Inequalities

Solve the inequality: -3x>-60

Possible Answers:

x>-57

x>20

x<20

$x \geq 20$

$x\leq20$

Correct answer:

x<20

Explanation:

Divide by negative three on both sides.

$\frac{-3x}{-3}>\frac{-60}{-3}$

Remember that since we are dividing by a negative sign, we will need to switch the sign.

The answer is: x<20

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Example Question #113 : Equations / Inequalities

Solve the inequality: -3x+6>24

Possible Answers:

$x\geq6$

x>-6

x<-6

$x\leq-6$

$x\leq6$

Correct answer:

x<-6

Explanation:

Subtract six on both sides.

-3x+6-6>24-6

-3x>18

Divide by negative three on both sides. When we divide by a negative number, we will need to switch the direction of the sign.

$\frac{-3x}{-3}>\frac{18}{-3}$

Simplify both sides and switch the sign.

The answer is: x<-6

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Example Question #112 : Systems Of Inequalities

Solve the following inequality: 5x>-30

Possible Answers:

x<-6

x>-25

x<6

x>6

x>-6

Correct answer:

x>-6

Explanation:

Isolate the x-variable by dividing by five on both sides. There is no need to switch the sign in this scenario.

$\frac{5x}{5}>\frac{-30}{5}$

Simplify both fraction.

The answer is: x>-6

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Example Question #35 : How To Find The Solution To An Inequality With Division

Solve the inequality: -9y <-81

Possible Answers:

$y\geq9$

y<-90

y>-9

y<-71

y>9

Correct answer:

y>9

Explanation:

To solve this inequality, divide both sides by negative nine.

$\frac{-9y}{-9} <\frac{-81}{-9}$

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

Simplify both sides.

The answer is: y>9

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Algebra 1 : Systems of Inequalities

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #2234 : Algebra 1

Example Question #27 : How To Find The Solution To An Inequality With Division

Example Question #111 : Equations / Inequalities

Example Question #29 : How To Find The Solution To An Inequality With Division

Example Question #2241 : Algebra 1

Example Question #31 : How To Find The Solution To An Inequality With Division

Example Question #111 : Systems Of Inequalities

Example Question #113 : Equations / Inequalities

Example Question #112 : Systems Of Inequalities

Example Question #35 : How To Find The Solution To An Inequality With Division

All Algebra 1 Resources

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