# Solving Inequalities

 Our Algebra 1 tutorial software program contains over 60 topic areas. One of them is Solving Inequalities, and this page summarizes the main ideas of this topic. This page is intended for review, and is not a substitute for the interactive, self-paced tutorials of the MathTutor algebra 1 software program.

General Explanation

In order to solve an equation we must bring the variable to one side of the equation by itself. 3x + 2 = 11 is solved when we say x = 3.

To SOLVE AN INEQUALITY we must also bring the variable to one side of the inequality by itself.

Consider:
` x + 5 > 9`
This is equivalent to
``` x + 5 - 5 > 9 - 5 or
x > 4```
The inequality is solved in the final expression because the variable is by itself on one side.

To solve inequalities we can use the rules we learned previously.

• For x + a < c:
```x + a - a < c - a or
x < c - a
```
• For x - a < c:
```x - a + a < c + a or
x < c + a
```
• For 4x < c:
```4x/4 < c/4 or
x < c/4
```
• For 7 > -2x:
```7/-2 < -2x/-2 or
-7/2 < x```
When we multiply or divide both sides of the inequality by a negative number, we must change the direction of the inequality sign.

Sample Problem

Solve the inequality:
```4x - 3 > 6
```

Solution

First, we add 3 to each side:
```4x - 3 + 3 > 6 + 3
4x > 9
```
Now, to get x by itself, we divide each side by 4:
```4x/4 > 9/4
x > 9/4
```
So our final answer is x > 9/4.