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

Study concepts, example questions & explanations for Algebra 1

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Example Questions

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

Solve this inequality:

Possible Answers:

Correct answer:

Explanation:

First, add  to both sides:

, or

.

Then, add 2 to both sides:

, or

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

which simplifies to:

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

Solve for :

Possible Answers:

None of the other answers

Correct answer:

Explanation:

To solve the inequality, simply move the 's to one side and the integers to the other (i.e. subtract from both sides and add 9 to both sides). This gives you .

Example Question #51 : Equations / Inequalities

Solve for :

Possible Answers:

Correct answer:

Explanation:

Subtracting and adding 3 to both sides of the equation of will give you . Divide both sides by 2 to get .

Example Question #52 : Equations / Inequalities

Which value of is in the solution set of the inequality ?

Possible Answers:

Correct answer:

Explanation:

Add and subtract 2 from both sides of to get . Then, divide both sides by 3 to get a solution of . The only answer choice that is greater than 5 is 6.

Example Question #53 : Equations / Inequalities

Find the solution set for :

Possible Answers:

Correct answer:

Explanation:

Note the switch in inequality symbols when the numbers are multiplied by a negative number.

or, in interval notation, 

Example Question #54 : Equations / Inequalities

Solve the inequality:

Possible Answers:

No solution

Correct answer:

Explanation:

Combine like-terms on the left side of the inequality: . Next, isolate the variable: .

Therefore the answer is

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

Solve:

Possible Answers:

None of the other answers are correct.

Correct answer:

Explanation:

Subtract 2 from each side:

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

Solve for :

 

Possible Answers:

Correct answer:

Explanation:

This inequality can be solved just like an equation.

Add 4 to both sides:

2x > 11

Then divide by 2:

x > 11/2 = 5.5

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

Solve the inequality:

Possible Answers:

Correct answer:

Explanation:

First, combine like terms on a single side of the inequality. On the right side of the inequality, combine the terms to obtain .

Next, we want to get all the variables on the left side of the inequality and all of the constants on the right side of the inequality. Add 4 to both sides and subtract  from both sides to get .

Finally, to isolate the variable, divide both sides by 12 to produce the final answer,

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

Solve:  

Possible Answers:

Correct answer:

Explanation:

To solve , isolate the variable by adding three on both sides.

The correct answer is:  

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