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

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Example Question #31 : Equations / Inequalities

Find the solution to the inequality: $9\geq x+18$

Possible Answers:

$x\geq9$

$x\geq-9$

$x\leq27$

$x\leq9$

$x\leq-9$

Correct answer:

$x\leq-9$

Explanation:

In order to isolate the variable, we need to move the 18 to the left side by subtracting 18 on both sides.

$9-18\geq x+18-18$

Simplify both sides.

$-9\geq x$

This indicates that must be less than or equal to negative nine.

Rewrite the inequality so that the is on the left side, and the number is on the right side.

The answer is: $x\leq-9$

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Example Question #32 : Equations / Inequalities

Solve the inequality: x+13<-13

Possible Answers:

x<-26

x>-26

x<0

$x\leq0$

x>0

Correct answer:

x<-26

Explanation:

In order to isolate the x-variable, simply subtract 13 from both sides of the inequality.

x+13-13<-13-13

Simplify both sides of the inequality.

x<-26

There is no need to switch the sign.

The answer is: x<-26

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Example Question #31 : Systems Of Inequalities

Solve the inequality: x+30>-25

Possible Answers:

x>-55

x>5

x<55

x>-5

x<5

Correct answer:

x>-55

Explanation:

In order to solve this inequality, we will need to subtract 30 from both sides of the equation.

x+30-30>-25-30

Simplify both sides of the equation.

The answer is: x>-55

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Example Question #41 : Systems Of Inequalities

Solve: x+13>-13

Possible Answers:

x<-26

x<0

x>26

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 #42 : Equations / Inequalities

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

Possible Answers:

$y\leq-5$

y<5

y>5

y<-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 #41 : Systems Of Inequalities

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

Possible Answers:

x<-27

$x\leq27$

$x\leq-27$

$x\geq -27$

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 #44 : Equations / Inequalities

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

Possible Answers:

$x\leq -28$

x<-14

x<-28

$x\geq -28$

$x\leq -14$

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 #45 : Equations / Inequalities

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

Possible Answers:

$x\leq-1$

x<1

x>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 #42 : Systems Of Inequalities

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

Possible Answers:

$x\leq -36$

x<-36

$x\geq-36$

x>36

$x\geq36$

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 #43 : Systems Of Inequalities

Solve the following inequality: x+9>-93

Possible Answers:

x>-102

$x\leq-84$

x>-84

x<-102

x<-84

Correct answer:

x>-102

Explanation:

Subtract nine on both sides.

x+9-9>-93-9

Simplify both sides.

The answer is: x>-102

Report an Error

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

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #31 : Equations / Inequalities

Example Question #32 : Equations / Inequalities

Example Question #31 : Systems Of Inequalities

Example Question #41 : Systems Of Inequalities

Example Question #42 : Equations / Inequalities

Example Question #41 : Systems Of Inequalities

Example Question #44 : Equations / Inequalities

Example Question #45 : Equations / Inequalities

Example Question #42 : Systems Of Inequalities

Example Question #43 : Systems Of Inequalities

All Algebra 1 Resources

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