Inequalities Introduction Algebra Seminar

2012-2013

Inequalities vs. Equations

Just like with equations, the solution to an inequality is a value that makes the inequality true.

You can solve inequalities in the same way you can solve equations.

You may multiply or divide both sides of an inequality by any positive number.

Solving Inequalities

* Solving inequalities follows the same procedures as solving equations.

* There are a few special things to consider with inequalities:

* We need to look carefully at the inequality sign.* We also need to graph the solution set.

Review of Inequality Signs

> greater than< less than

greater than or equal

less than or equal

Graphing the solutions

> Graph any number greater than. . . open circle, line to the right

< Graph any number less than. . . open circle, line to the left

Graph any number greater than or equal to. . . closed circle, line to the right

Graph any number less than or equal to. . . closed circle, line to the left

Setting up the number line:

Create a line that extends infinitely in both the positive and negative directionsCenter the line around your focus numberIs it open or closed?Shade to the left or right?

Graphing the inequality:

x < 3

● Things to decide:

●Will it be an open or closed circle?

●Will we shade to the left or to the right?

• Open circle, line to the left.

30

Lets make some graphs!

x > -5

x < -7

Some harder ones to try:

1.

2.

3.

One special case!

* Sometimes you may have to reverse the direction of the inequality sign!!

* That only happens when you multiply or divide both sides of the

inequality by a negative number.

Examples:

1. 3x < 12

2. -5x > 20

Summary

Many simple inequalities can be solved and graphed on the number line.

If the variable is not isolated we can often simplify by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own.

Summary

But these things will change direction of the inequality:– Multiplying or dividing both sides by a

negative number– Swapping left and right hand sides

Don't multiply or divide by a variable (unless you know it is always positive or always negative)