# Algebra 1 : Systems of Inequalities

## Example Questions

### 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:

Explanation:

Divide by three on both sides.

Reduce both sides.  For the right side, dividing by three is similar to multiplying by one-third.

Simplify.

### Example Question #31 : How To Find The Solution To An Inequality With Division

Find the solution of the inequality:

Explanation:

To isolate the x-variable, we will need to divide by negative four on both sides.  This is the same as multiplying negative one fourth on both sides.

Since we have a negative in front, we will also need to switch the sign.

Simplify both sides of the equation and switch the sign.

### Example Question #32 : How To Find The Solution To An Inequality With Division

Solve the inequality:

Explanation:

Divide by negative three on both sides.

Remember that since we are dividing by a negative sign, we will need to switch the sign.

### Example Question #33 : How To Find The Solution To An Inequality With Division

Solve the inequality:

Explanation:

Subtract six on both sides.

Divide by negative three on both sides.  When we divide by a negative number, we will need to switch the direction of the sign.

Simplify both sides and switch the sign.

### Example Question #34 : How To Find The Solution To An Inequality With Division

Solve the following inequality:

Explanation:

Isolate the x-variable by dividing by five on both sides.  There is no need to switch the sign in this scenario.

Simplify both fraction.

### Example Question #35 : How To Find The Solution To An Inequality With Division

Solve the inequality: