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

## Example Questions

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

Find the solution set of the compound inequality:

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

Find the solution set for :

Explanation:

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

or, in interval form:

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

Solve for :

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 #14 : How To Find The Solution To An Inequality With Division

Solve for :

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 #15 : How To Find The Solution To An Inequality With Division

Find the solution set for the inequality.

Does not exist.

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 #16 : How To Find The Solution To An Inequality With Division

Solve for :

None of the other answers are correct.

Explanation:

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

Divide both sides by 2:

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

### Example Question #17 : How To Find The Solution To An Inequality With Division

Find the solution set to the compound inequality:

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

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

Solve the following inequality.

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 #19 : How To Find The Solution To An Inequality With Division

Solve the inequality

.

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 #20 : How To Find The Solution To An Inequality With Division

Solve the inequality.