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Algebra 1 : Systems of Inequalities

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Example Questions

Example Question #41 : Systems Of Inequalities

Solve: x+13>-13

Possible Answers:

x>26

x>-26

x<0

x<26

x<-26

Correct answer:

x>-26

Explanation:

Solve by subtracting 13 on both sides of the inequality.

x+13-13>-13-13

Simplify both sides. When subtracting a number from a negative number, the number will be increasingly negative.

The answer is: x>-26

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Example Question #15 : How To Find The Solution To An Inequality With Subtraction

Solve the inequality: 2y+3>18+5y

Possible Answers:

y<5

y>5

y<-5

$y\leq-5$

y>-5

Correct answer:

y<-5

Explanation:

To solve this inequality, we will need to group the variables on one side, and the constants on the other.

Subtract on both sides to move it to the right side.

2y+3-(2y)>18+5y-(2y)

Simplify both sides.

3>18+3y

Subtract 18 from both sides.

3-18>18+3y-18

Simplify both sides.

-15>3y

Divide by three on both sides.

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

Reduce the fractions.

The answer is: y<-5

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Example Question #15 : How To Find The Solution To An Inequality With Subtraction

Solve the inequality: x+9>-12-6

Possible Answers:

x>-27

$x\geq -27$

$x\leq-27$

$x\leq27$

x<-27

Correct answer:

x>-27

Explanation:

Simplify the right side of the inequality.

x+9>-18

Subtract nine on both sides.

x+9-9>-18-9

Simplify both sides of the inequality.

x>-27

The answer is: x>-27

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Example Question #16 : How To Find The Solution To An Inequality With Subtraction

Solve the following inequality: $x+7\leq -21$

Possible Answers:

$x\geq -28$

$x\leq -14$

x<-28

$x\leq -28$

x<-14

Correct answer:

$x\leq -28$

Explanation:

In order to isolate the variable, subtract 7 from both sides of the inequality.

$x+7-7\leq -21-7$

Simplify both sides.

$x\leq -28$

The answer is: $x\leq -28$

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Example Question #42 : Systems Of Inequalities

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

Possible Answers:

x<-1

x>1

$x\leq-1$

x>-1

x<1

Correct answer:

x<-1

Explanation:

Group the integers on the left side and the values on the right side.

Subtract three on both sides.

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

Simplify both sides.

x-1>2x

Subtract on both sides.

x-1-x>2x-x

Simplify both sides.

-1>x

The answer is: x<-1

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Example Question #18 : How To Find The Solution To An Inequality With Subtraction

Solve the inequality: $x+6\leq -30$

Possible Answers:

$x\geq-36$

x<-36

$x\leq -36$

$x\geq36$

x>36

Correct answer:

$x\leq -36$

Explanation:

Solve this inequality by subtracting six from both sides. This will isolate the x-variable.

$x+6-6\leq -30-6$

Simplify both sides. A negative number subtracting a number will be further way from zero.

The answer is: $x\leq -36$

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Example Question #42 : Systems Of Inequalities

Solve the following inequality: x+9>-93

Possible Answers:

x>-102

x<-84

$x\leq-84$

x>-84

x<-102

Correct answer:

x>-102

Explanation:

Subtract nine on both sides.

x+9-9>-93-9

Simplify both sides.

The answer is: x>-102

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

Solve the inequality: 3+x>2x+6

Possible Answers:

x<-3

x>-3

x<-6

x>3

x<3

Correct answer:

x<-3

Explanation:

Group the integers and the terms with the x-variables.

Subtract six from both sides.

3+x-6>2x+6-6

Simplify both sides.

x-3>2x

Subtract from both sides.

x-3-x>2x-x

Simplify both sides.

-3>x

We can rewrite this inequality.

The answer is: x<-3

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

Solve the inequality: 3+x<2x+5

Possible Answers:

$x\geq-2$

x>-2

x<-2

x<2

x>2

Correct answer:

x>-2

Explanation:

Solve the inequality by subtracting 5 on both sides.

3+x-5<2x+5-5

Simplify both sides.

x-2<2x

Subtract on both sides.

x-2-x<2x-x

Simplify both sides.

-2<x

The answer is: x>-2

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Example Question #43 : Equations / Inequalities

Solve this inequality:

5x -2 < 8 - x

Possible Answers:

$x < \frac{5}{2}$

$x > \frac{5}{3}$

$x < \frac{5}{3}$

$x < \frac{7}{3}$

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

Correct answer:

$x < \frac{5}{3}$

Explanation:

First, add to both sides:

5x -2 +x < 8 - x + x , or

6x -2 < 8 .

Then, add 2 to both sides:

6x - 2 + 2 < 8 + 2 , or

6x < 10

Finally, divide both sides by 6 to get the answer:

$x < \frac{10}{6}$

which simplifies to:

$x < \frac{5}{3}$

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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 #41 : Systems Of Inequalities

Example Question #15 : How To Find The Solution To An Inequality With Subtraction

Example Question #15 : How To Find The Solution To An Inequality With Subtraction

Example Question #16 : How To Find The Solution To An Inequality With Subtraction

Example Question #42 : Systems Of Inequalities

Example Question #18 : How To Find The Solution To An Inequality With Subtraction

Example Question #42 : Systems Of Inequalities

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

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

Example Question #43 : Equations / Inequalities

All Algebra 1 Resources

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