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Algebra 1 : Systems of Inequalities

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Example Question #81 : Equations / Inequalities

Solve the inequality: 6<x-19

Possible Answers:

x<-25

x>-25

x>-13

x>25

x<25

Correct answer:

x>25

Explanation:

Solve by adding nineteen on both sides.

6+19<x-19+19

Simplify both sides.

25<x

This is also the same as: x>25

The answer is: x>25

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

Solve the inequality: $z-3\geq 16$

Possible Answers:

z<19

$z\leq13$

$z\geq 19$

$z\geq13$

$z\leq 19$

Correct answer:

$z\geq 19$

Explanation:

In order to solve this inequality, add three on both sides.

$z-3+3\geq 16+3$

Simplify both sides of the inequality.

The answer is: $z\geq 19$

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Example Question #81 : Equations / Inequalities

Solve the following inequality: $-x-9\leq-6$

Possible Answers:

$x\geq -3$

$x\leq 15$

$x\leq 3$

$x\leq -3$

$x\geq 3$

Correct answer:

$x\geq -3$

Explanation:

Add six on both sides

$-x-9+6\leq-6+6$

Simplify both sides.

$-x-3\leq0$

Add on both sides.

$-x-3+x\leq0+x$

Simplify the left side. Since we are adding a negative variable, it is not necessary to change the sign.

$-3\leq x$

The answer is: $x\geq -3$

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Example Question #81 : Systems Of Inequalities

Solve the inequality: -3-3x>-2x

Possible Answers:

x<3

$x\leq-3$

x<-3

x>-3

$x\geq-3$

Correct answer:

x<-3

Explanation:

Group the x-variables by adding on both sides of the equation.

-3-3x+3x>-2x+3x

Simplify both sides of the equation.

-3>x

Since we did not divide by a negative number, we do not need to switch the direction of the sign.

The answer is: x<-3

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Example Question #33 : How To Find The Solution To An Inequality With Addition

Solve the inequality: x-15<66

Possible Answers:

x<51

x>-81

x<81

x<-81

x<-51

Correct answer:

x<81

Explanation:

In order to isolate the x-variable, add 15 on both sides of equation.

x-15+15<66+15

Simplify both sides of the inequality.

The answer is: x<81

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

Solve for :

3x-1>x+7

Possible Answers:

x<4

x>4

None of the other answers

x<2

x>2

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:

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

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

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

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

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

Give the solution set of the inequality:

-4x + 17 > 81

Possible Answers:

(-16,16)

$(-\infty ,16)$

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

The set of all real numbers

$(-\infty ,-16)$

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

Give the solution set of the inequality:

$-5x + 17 \geq 82$

Possible Answers:

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

The inequality has no solution.

$[-13,\infty)$

(-13,13)

$(-\infty , -13]$

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

Give the solution set of the inequality:

$-5x + 27 \leq 62$

Possible Answers:

The inequality has no solution.

$[7,\infty )$

$[-7,\infty )$

$(-\infty , -7]$

[-7,7]

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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Algebra 1 : Systems of Inequalities

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #81 : Equations / Inequalities

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

Example Question #81 : Equations / Inequalities

Example Question #81 : Systems Of Inequalities

Example Question #33 : How To Find The Solution To An Inequality With Addition

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

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