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

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Example Questions

Example Question #1 : How To Find The Solution To An Inequality With Division

Solve for :

3x-1>x+7

Possible Answers:

x>2

x<2

x<4

x>4

None of the other answers

Correct answer:

x>4

Explanation:

To solve for , separate the integers and 's by adding 1 and subtracting from both sides to get 2x>8 . Then, divide both sides by 2 to get x>4 . Since you didn't divide by a negative number, the sign does not need to be reversed.

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Example Question #2 : How To Find The Solution To An Inequality With Division

Solve the following: -2x+3>4

Possible Answers:

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

$x<-\frac{7}{2}$

$x>-\frac{7}{2}$

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

Correct answer:

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

Explanation:

-2x+3-3>4-3

-2x>1

$\frac{-2x}{-2}<\frac{1}{-2}$ Don't forget to change the direction of the inequality sign when dividing by a negative number!

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

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Example Question #2 : How To Find The Solution To An Inequality With Division

Give the solution set of the inequality:

-4x + 17 > 81

Possible Answers:

The set of all real numbers

$(-\infty ,-16)$

$\left (-16, \infty \right )$

$(-\infty ,16)$

(-16,16)

Correct answer:

$(-\infty ,-16)$

Explanation:

-4x + 17 > 81

-4x + 17 -17 > 81 -17

-4x > 64

$-4x \div (-4)< 64 \div (-4)$

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

x < -16

or, in interval form,

$(-\infty ,-16)$

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Example Question #3 : How To Find The Solution To An Inequality With Division

Give the solution set of the inequality:

$-5x + 17 \geq 82$

Possible Answers:

$(-\infty , -13]$

$[-13,\infty)$

$\left [13, \infty \right )$

The inequality has no solution.

(-13,13)

Correct answer:

$(-\infty , -13]$

Explanation:

$-5x + 17 \geq 82$

$-5x + 17 -17 \geq 82-17$

$-5x \geq 65$

$-5x \div (-5) \leq 65\div (-5)$

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

$x \leq -13$

or, in interval form,

$(-\infty , -13]$

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Example Question #4 : How To Find The Solution To An Inequality With Division

Give the solution set of the inequality:

$-5x + 27 \leq 62$

Possible Answers:

$(-\infty , -7]$

$[7,\infty )$

[-7,7]

The inequality has no solution.

$[-7,\infty )$

Correct answer:

$[-7,\infty )$

Explanation:

$-5x + 27 \leq 62$

$-5x + 27 -27 \leq 62-27$

$-5x \leq 35$

$-5x \div (-5) \leq 35\div (-5)$

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

$x \geq -7$

or, in interval form,

$[-7,\infty )$

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Example Question #5 : How To Find The Solution To An Inequality With Division

Give the solution set of the inequality:

-4x - 11 < 57

Possible Answers:

(-17,17)

$(-\infty,-17 )$

$(-17,\infty )$

$(17,\infty )$

The set of all real numbers

Correct answer:

$(-17,\infty )$

Explanation:

-4x - 11 < 57

-4x - 11 + 11 < 57 + 11

-4x < 68

$-4x \div (-4) > 68 \div (-4)$

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

x > -17

or, in interval form,

$(-17,\infty )$

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Example Question #6 : How To Find The Solution To An Inequality With Division

Give the solution set of the inequality:

-4x + 11 < 67

Possible Answers:

The set of all real numbers

$(-14, \infty )$

$(-\infty ,14 )$

$(-\infty ,-14 )$

(-14,14)

Correct answer:

$(-14, \infty )$

Explanation:

-4x + 11 < 67

-4x + 11 - 11 < 67- 11

-4x < 56

$-4x \div (-4) > 56 \div (-4)$

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

x > -14

or, in interval form,

$(-14, \infty )$

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Example Question #7 : How To Find The Solution To An Inequality With Division

Solve for :

2-6x>10-2x

Possible Answers:

x>-2

x>2

x<2

x<-2

None of the other answers

Correct answer:

x<-2

Explanation:

First, add and subtract from both sides of the inequality to get -4x>8 .

Then, divide both sides by and reverse the sign since you are dividing by a negative number.

This gives you x<-2 .

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Example Question #8 : How To Find The Solution To An Inequality With Division

Find the solution set to the following compound inequality statement:

$4y + 15 < 91 \textrm{ and } 7y -12 > 86$

Possible Answers:

(14,19)

$(-\infty , \infty )$

$(-\infty , 14) \cup (19, \infty )$

$(14, \infty )$

$(-\infty , 19)$

Correct answer:

(14,19)

Explanation:

Solve each of these two inequalities separately:

4y + 15 < 91

4y + 15 - 15 < 91- 15

4y < 76

$4y \div 4 < 76 \div 4$

y < 19 , or, in interval form, $(-\infty , 19)$

7y -12 > 86

7y -12 + 12 > 86 + 12

7y > 98

$7y \div 7 > 98 \div 7$

y > 14 , or, in interval form, $(14, \infty )$

The two inequalities are connected with an "and", so we take the intersection of the two intervals.

$(14, \infty ) \cap (-\infty , 19) = (14,19)$

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Example Question #9 : How To Find The Solution To An Inequality With Division

Solve for :

$0.4 x - 1.7 \geq -8.5$

Possible Answers:

The inequality has no solution.

$[1.7, \infty )$

$[-1.7, \infty )$

$[17, \infty )$

$[-17, \infty )$

Correct answer:

$[-17, \infty )$

Explanation:

$0.4 x - 1.7 \geq -8.5$

$0.4 x - 1.7 + 1.7 \geq -8.5+ 1.7$

$0.4 x \geq -6.8$

$0.4 x \div 0.4 \geq -6.8\div 0.4$

$x \geq -17$

or, in interval form, $[-17, \infty )$

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

Example Question #2 : How To Find The Solution To An Inequality With Division

Example Question #2 : How To Find The Solution To An Inequality With Division

Example Question #3 : How To Find The Solution To An Inequality With Division

Example Question #4 : How To Find The Solution To An Inequality With Division

Example Question #5 : How To Find The Solution To An Inequality With Division

Example Question #6 : How To Find The Solution To An Inequality With Division

Example Question #7 : How To Find The Solution To An Inequality With Division

Example Question #8 : How To Find The Solution To An Inequality With Division

Example Question #9 : How To Find The Solution To An Inequality With Division

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