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

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Example Questions

Example Question #21 : How To Find The Solution To An Inequality With Division

Simplify the following inequality:

-3x>6

Possible Answers:

$x\leq-2$

x>-2

x<-2

$x\geq-2$

Correct answer:

x<-2

Explanation:

To do this question all you need to do is divide both sides by

So, $\frac{-3x}{-3}> \frac{6}{-3}$

Which gives you: x<-2

It is important to remember that the greater than sign flips to less than when dividing by a negative number.

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Example Question #22 : How To Find The Solution To An Inequality With Division

Solve the following inequality for :

4x+3<2x-13

Possible Answers:

x<-5

x<8

x>8

x>5

x<-8

Correct answer:

x<-8

Explanation:

4x+3<2x-13

First, using the additive inverses, isolate the variables and constants on either side of the equation. In other words, subtract from both sides, and subtract from both sides. This leaves you with:

2x<-16

Now use the multiplicative inverse (divide by ) to solve the inequality.

Keep in mind that we do not flip the inequality symbol because the number we were dividing by is positive.

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Example Question #104 : Equations / Inequalities

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

Find all of the solutions to this inequality.

Possible Answers:

[0,7]

$(-\infty , 28)$

$[\infty ,28]$

$[-\infty , 28)$

$(\infty, 7)$

Correct answer:

$(-\infty , 28)$

Explanation:

To solve an inequality, isolate the variable on one side with all other constants on the other side. To accomplish this, perform opposite operations to manipulate the inequality.

First, isolate the x by multiplying each side by four.

Whatever you do to one side you must also do to the other side.

${\color{Blue} 4}(\frac{x}{4})<(7){\color{Blue} 4}$

This gives you:

x<28

The answer, therefore, is $(-\infty , 28)$ .

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Example Question #105 : Equations / Inequalities

Solve the following inequality: -2x+4>0

Possible Answers:

x>2

x<8

x<-2

x<2

x>-2

Correct answer:

x<2

Explanation:

To isolate the variable, first subtract four on both sides.

-2x+4-4>0-4

Simplify the left and the right side of the equation.

-2x>-4

Divide by negative two on both sides. When dividing by a negative number, be sure to switch the sign.

$\frac{-2x}{-2}<\frac{-4}{-2}$

x<2

The answer is: x<2

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Example Question #22 : How To Find The Solution To An Inequality With Division

Solve: -2x>12

Possible Answers:

x>-6

x<-6

x<6

$x\leq-6$

$x\geq-6$

Correct answer:

x<-6

Explanation:

Divide by negative two on both sides. When dividing a negative number, switch the sign of the inequality.

$\frac{-2x}{-2}>\frac{12}{-2}$

Simplify both sides of the equation.

The answer is: x<-6

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Example Question #111 : Equations / Inequalities

Solve the inequaltiy: -9x<99

Possible Answers:

x>-108

x>-11

x<-11

x>11

x<-108

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 #112 : Systems Of Inequalities

Find the solution: -6x<52

Possible Answers:

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

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

x<-9

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

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

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 #113 : Systems Of Inequalities

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

Possible Answers:

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

y<3

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

y>3

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

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

Example Question #22 : How To Find The Solution To An Inequality With Division

Example Question #104 : Equations / Inequalities

Example Question #105 : Equations / Inequalities

Example Question #22 : How To Find The Solution To An Inequality With Division

Example Question #111 : Equations / Inequalities

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

Example Question #112 : Systems Of Inequalities

Example Question #113 : Systems Of Inequalities

Example Question #2241 : Algebra 1

All Algebra 1 Resources

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