ALGEBRA

REVIEW

The Real Number Line

negative numbers are to the left of 0

positive numbers are to the right of 0

a > 0 means a is positivea < 0 means a is negative

A – sign, such as the one in -1, tells us that the number is to the

left of 0 on the number line. A + sign or no sign tells us that

a number lies to the right of 0 on the number line. For example, 3 and +3 both mean “positive

three”

Helpful Hint

The Real Number Line

negative numbers are to the left of 0

positive numbers are to the right of 0

a < b is read "a is less than b" and means a is further to the left on the number line than b

a > b is read "a is greater than b" and means a is further to the right on the number line than b

These are called strict inequalities

a b or a b are nonstrict inequalities and mean besides being less than or greater than b, a can equal b.

a > 0 means a is positivea < 0 means a is negative

2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 0 4 6 8 [

1x

Because the inequality is "greater than or equal to" the solution can equal the endpoint. A square bracket means it can equal the endpoint.

squared end bracket

We can graph inequalities on the number line.

Let's look at a different inequality sign.

2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 0 4 6 8 )

1x

Since this says "less than" we make the arrow go the other way. Since it doesn't say "or equal to" the solution cannot equal the endpoint. A rounded bracket means it cannot equal the endpoint.

rounded end bracket

Absolute value is the distance from zero. It doesn't matter whether we are in the positive direction or the negative direction, we just care about how far away we are.

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

44

4 units away from 0

44

4 units away from 0

If we want to know how far apart points on the number line are, we can take the difference between them and then take the absolute value.

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

5 3 8

8 units apart

What is the distance from -5 to 3?

Since the absolute value of a number is the number’s

distance from 0, the absolute value of a number is always 0 or

positive. It is never negative

0 0 6 6

Helpful Hints

Homework for 2.1Pg. 101-103

1-81 odd