# Algebra 1 : Systems of Inequalities

## Example Questions

### Example Question #81 : Equations / Inequalities

Solve the inequality:

Explanation:

Solve by adding nineteen on both sides.

Simplify both sides.

This is also the same as:

### Example Question #81 : Systems Of Inequalities

Solve the inequality:

Explanation:

In order to solve this inequality, add three on both sides.

Simplify both sides of the inequality.

### Example Question #81 : Equations / Inequalities

Solve the following inequality:

Explanation:

Add six on both sides

Simplify both sides.

Add  on both sides.

Simplify the left side.  Since we are adding a negative variable, it is not necessary to change the sign.

### Example Question #81 : Systems Of Inequalities

Solve the inequality:

Explanation:

Group the x-variables by adding  on both sides of the equation.

Simplify both sides of the equation.

Since we did not divide by a negative number, we do not need to switch the direction of the sign.

### Example Question #82 : Systems Of Inequalities

Solve the inequality:

Explanation:

In order to isolate the x-variable, add 15 on both sides of equation.

Simplify both sides of the inequality.

### 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 #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 #4 : 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 #1 : How To Find The Solution To An Inequality With Division

Give the solution set of the inequality:

The inequality has no solution.