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

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #91 : Equations / Inequalities

Find the solution set of the compound inequality:

 

Possible Answers:

Correct answer:

Explanation:

Solve each inequality separately:

or, in interval form, 

 

or, in interval form, 

 

Since these statements are connected by an "or", we are looking for the union of the intervals. Since the intervals are disjoint, we can simply write this as 

Example Question #11 : How To Find The Solution To An Inequality With Division

Find the solution set for :

Possible Answers:

Correct answer:

Explanation:

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

or, in interval form:

Example Question #2222 : Algebra 1

Solve for :

Possible Answers:

Correct answer:

Explanation:

To solve the inequality, you must first separate the integers and the 's. Subtract  and add  to both sides of the inequality to get 

.

Then, divide both sides by  to get 

.

Since you are not dividing by a negative number, the sign does not need to be reversed.

Example Question #2223 : Algebra 1

Solve for :

Possible Answers:

None of the other answers

Correct answer:

Explanation:

First, use the distributive property to simplify the right side of the inequality: 

.

Then, add  and subtract  from both sides of the inequality to get 

.

Finally, divide  from both sides to get .

Example Question #92 : Equations / Inequalities

Find the solution set for the inequality.

Possible Answers:

Does not exist.

Correct answer:

Explanation:

Subtract 100 from each side:

Divide both sides by -2:

(Note that the inequality symbol switched when we divided by a negative number.)

Example Question #101 : Equations / Inequalities

Solve for :

Possible Answers:

None of the other answers are correct.

Correct answer:

Explanation:

To solve this inequality, get the 's to one side of the equation and the integers to the other side. 

Add 1 to both sides:

Divide both sides by 2: 

(Since we are not dividing by a negative number, there is no need to reverse the sign.)

Example Question #102 : Systems Of Inequalities

Find the solution set to the compound inequality:

 

Possible Answers:

Correct answer:

Explanation:

Solve each of these two inequalities separately:

, or in interval form, 

 

 

(Note the flipping of the inequality because of the division by a negative number.)

, or in interval form, 

 

The question asks about the intersection of the two intervals:

The intersection is the area of the number line that the two sets share, or .

Example Question #12 : How To Find The Solution To An Inequality With Division

Solve the following inequality.

Possible Answers:

Correct answer:

Explanation:

To solve this inequality, move all the terms with  on one side and all other terms on the other side, then solve for x.

Example Question #13 : How To Find The Solution To An Inequality With Division

Solve the inequality

.

Possible Answers:

Correct answer:

Explanation:

Inequalities are treated as equalities when it comes to balancing, with the exception of division by a negative number (then flip the greater/less than symbol).

The question is asking for the solved inequality isolating . Combine like terms across sides by adding or subtracting same value to both sides.

Example Question #2231 : Algebra 1

Solve the inequality.

Possible Answers:

Correct answer:

Explanation:

Use the properties of inequalities to balance the inequality and isolate .

First subtract three from both sides.

Next, divide by four.

Since no division or multiplication of a negative number occurred, the inequality sign remains the same.

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