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

## Example Questions

### Example Question #21 : How To Find The Solution To An Inequality With Division

Simplify the following inequality:

Explanation:

To do this question all you need to do is divide both sides by

So,

Which gives you:

It is important to remember that the greater than sign flips to less than when dividing by a negative number.

### Example Question #22 : How To Find The Solution To An Inequality With Division

Solve the following inequality for :

Explanation:

First, using the additive inverses, isolate the variables and constants on either side of the equation. In other words, subtract  from both sides, and subtract  from both sides. This leaves you with:

Now use the multiplicative inverse (divide by ) to solve the inequality.

Keep in mind that we do not flip the inequality symbol because the number we were dividing by is positive.

### Example Question #23 : How To Find The Solution To An Inequality With Division

Find all of the solutions to this inequality.

Explanation:

To solve an inequality, isolate the variable on one side with all other constants on the other side. To accomplish this, perform opposite operations to manipulate the inequality.

First, isolate the x by multiplying each side by four.

Whatever you do to one side you must also do to the other side.

This gives you:

### Example Question #24 : How To Find The Solution To An Inequality With Division

Solve the following inequality:

Explanation:

To isolate the  variable, first subtract four on both sides.

Simplify the left and the right side of the equation.

Divide by negative two on both sides.  When dividing by a negative number, be sure to switch the sign.

### Example Question #25 : How To Find The Solution To An Inequality With Division

Solve:

Explanation:

Divide by negative two on both sides.  When dividing a negative number, switch the sign of the inequality.

Simplify both sides of the equation.

### Example Question #26 : How To Find The Solution To An Inequality With Division

Solve the inequaltiy:

Explanation:

Divide both sides by negative nine.  When we divide by a negative sign, be sure to switch the sign.

Simplify both sides.

### Example Question #27 : How To Find The Solution To An Inequality With Division

Solve:

Explanation:

We will need to isolate the term with the x variable.

First subtract three from both sides.

Simplify both sides of the inequality.

Divide by a negative three on both sides.  This will change switch the sign.

Simplify both sides.

### Example Question #28 : How To Find The Solution To An Inequality With Division

Find the solution:

Explanation:

Divide by negative six on both sides of the inequality.

Simplify both sides.  When dividing by a negative, the sign will switch.

Rewrite the numerator and denominator with common factors.

Cancel the two on the numerator and denominator.

### Example Question #29 : How To Find The Solution To An Inequality With Division

Solve the inequality:

Explanation:

In order to isolate the y variable, divide by negative nine on both sides.   When dividing by a negative sign, the sign will switch directions.

Simplify both sides.  When dividing by a negative nine, we can rewrite that as multiplying by negative one-ninth.

Simplify the right side.

### Example Question #30 : How To Find The Solution To An Inequality With Division

Solve the inequality: