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

## Example Questions

← Previous 1 3 4

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

Solve for :

None of the other answers

Explanation:

To solve for , separate the integers and 's by adding 1 and subtracting from both sides to get . Then, divide both sides by 2 to get . Since you didn't divide by a negative number, the sign does not need to be reversed.

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

Solve the following:

Explanation:

Don't forget to change the direction of the inequality sign when dividing by a negative number!

### Example Question #83 : Equations / Inequalities

Give the solution set of the inequality:

The set of all real numbers

Explanation:

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

or, in interval form,

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

Give the solution set of the inequality:

The inequality has no solution.

Explanation:

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

or, in interval form,

### Example Question #83 : Systems Of Inequalities

Give the solution set of the inequality:

The inequality has no solution.

Explanation:

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

or, in interval form,

### Example Question #3 : How To Find The Solution To An Inequality With Division

Give the solution set of the inequality:

The set of all real numbers

Explanation:

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

or, in interval form,

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

Give the solution set of the inequality:

The set of all real numbers

Explanation:

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

or, in interval form,

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

Solve for :

None of the other answers

Explanation:

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

Then, divide both sides by and reverse the sign since you are dividing by a negative number.

This gives you .

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

Find the solution set to the following compound inequality statement:

Explanation:

Solve each of these two inequalities separately:

, or, in interval form,

, or, in interval form,

The two inequalities are connected with an "and", so we take the intersection of the two intervals.

Solve for :