Idiot\'s Guides Basic Math and Pre-Algebra

132 Part 2: Into the Unknown

Picturing the Solution

The solution of an equation is usually just one number, so when you say x = 5, it’s easy to under-

stand what that means. The solution of an inequality is a set of numbers, a collection that goes on

and on and includes whole numbers, rational numbers, and irrational numbers. When you write

x > 5, you’re describing a whole collection of numbers. It’s helpful to have a picture to understand it.

The solution set of an inequality can be graphed on the number line by shading the appropriate

portion of the line. You can graph the inequality x u 2 on the number line by putting a solid dot

on 2 and then shading all the numbers to the right of 2.

Start the graph of the inequality x > -4 by circling -4. Don’t fill in that circle, because you don’t

actually want -4, but you want everything less than -4. Then shade to the left.

Use an open circle if the inequality sign is > or < and a solid dot for inequalities containing e

or u.

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

x  2

12345678 910

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

x ,- 4

12345678 910

CHECK POINT

Graph the solution set of each inequality.

26. x > 6


27. t < -1


28. y u -3
    29. a e 2
    30. x > 0

The Least You Need to Know

• Solve equations by performing the opposite operations in the opposite order.


• Always simplify before trying to solve.


• In an equation, a variable usually represents just one number. In an inequality,
  a variable usually represents a set of numbers.


• Solve inequalities just like equations, but if you multiply or divide both sides by
  a negative number, reverse the inequality sign.