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Algebra 1 : How to find the solution to an inequality with division

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Example Questions

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

Solve the inequality: -3x>-60

Possible Answers:

$x \geq 20$

x<20

$x\leq20$

x>20

x>-57

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 #32 : How To Find The Solution To An Inequality With Division

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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Example Question #36 : How To Find The Solution To An Inequality With Division

Solve the following inequality: -12x<-36

Possible Answers:

x>3

x<-3

x<3

x>-3

$x\leq3$

Correct answer:

x>3

Explanation:

Divide by negative twelve on both sides of the inequality.

Dividing by a negative value requires changing the direction of the sign.

$\frac{-12x}{-12}<\frac{-36}{-12}$

Simplify both sides.

The answer is: x>3

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Example Question #37 : How To Find The Solution To An Inequality With Division

Solve the inequality: $-2x>-\frac{1}{3}$

Possible Answers:

$x<-\frac{1}{6}$

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

$x>\frac{1}{6}$

$x<\frac{1}{6}$

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

Correct answer:

$x<\frac{1}{6}$

Explanation:

Divide both sides by negative two. We will need to switch the direction of the sign.

$\frac{-2x}{-2}>\frac{-\frac{1}{3}}{-2}$

Simplify both sides and switch the sign. Rewrite the complex fraction such that dividing by a negative two is similar to multiplying by negative half.

$x< -\frac{1}{3} \cdot -\frac{1}{2}$

Multiply the fractions on the right.

The answer is: $x<\frac{1}{6}$

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Example Question #38 : How To Find The Solution To An Inequality With Division

Solve the inequality: $-\frac{1}{8}x>8$

Possible Answers:

$x>\frac{63}{8}$

x>-64

x<-1

$x\leq-64$

x<-64

Correct answer:

x<-64

Explanation:

Dividing by negative one-eighth is similar to multiplying by negative eight on both sides. Since we are dividing by a negative number, the sign will switch.

$-\frac{1}{8}x \cdot -8>8 \cdot -8$

Simplify both sides.

The answer is: x<-64

Dividing by negative one-eighth is similar to multiplying by negative eight on both sides. Since we are dividing by a negative number, the sign will switch.

$-\frac{1}{8}x \cdot -8>8 \cdot -8$

Simplify both sides.

The answer is: x<-64

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Algebra 1 : How to find the solution to an inequality with division

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

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

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

Example Question #113 : Equations / Inequalities

Example Question #32 : How To Find The Solution To An Inequality With Division

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

Example Question #36 : How To Find The Solution To An Inequality With Division

Example Question #37 : How To Find The Solution To An Inequality With Division

Example Question #38 : How To Find The Solution To An Inequality With Division

All Algebra 1 Resources

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