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INTEGERS AND EQUATIONS

Unit Overview

In this unit, you will review integers and the rules that apply to adding, subtracting,

multiplying and dividing these special numbers. You will also learn about equations and

how the Real Number Properties of Equality justify the steps to solve an equation. You

will also solve literal equations and formulas.

Comparing Integers

The set of whole numbers consists of 0, 1, 2, 3 ... and can be represented on a number

line. We can match each whole number with another number that is the same distance

from 0 but on the opposite side of 0.

-4 -3 -2 -1 0 1 2 3 4

If you take a look at the number line above, 3 or (positive 3) and -3 (negative 3) are on

opposite sides of 0 but the same distance from 0. These numbers are called opposites and

make up the set of integers. Integers are the set of positive and negative whole numbers.

Examples: Name the integer that is suggested by each situation.

a) The temperature is 5? below 0.

-5 Below 0 suggests a negative integer.

b) Emily's lemonade stand made a $24 profit.

24 A profit suggests a positive integer.

Integers (03:50)

To compare integers, we will use the symbol "" which means greater than. If you remember from the previous unit, these symbols

are called inequality signs. An inequality can either be true or false. For example, the

sentence 12 > 8 is true and the sentence 6 > 9 is false.

On a number line, the numbers increase as you move from left to right. For any two

numbers, the number that is farther to the right is the larger number and the number

farther to the left is the lesser number. Let's take a look at comparing some integers

using the number line below.

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

Write a true sentence using < or > in place of .

a) 3 9 3 < 9

Since 3 is to the left of 9 on the number line, 3 is less than 9.

b) -5 11 -5 < 11

Since -5 is to the left of 11 on the number line, -5 is less than 11.

c) -3 -6 -3 > -6

Since -3 is to the right of -6 on the number line, -3 is greater than -6.

Hint: An easy way to remember the direction of the inequality sign is that it always

points to the smaller number.

If you study the number line above, you will notice that the integers 5 and -5 are the

same distance from 0. This brings us to another algebraic concept called absolute value.

The absolute value of a number is the distance it is from 0, which means that the absolute

value will always be positive. Absolute value is symbolized by using two straight bars

around a number.

Example #1: 24 means the absolute value of 24, which is 24 because 24 is 24

units away from 0.

Example #2: -57 means the absolute value of -57, which is 57 because -57 is

57 units away from 0.

Stop! Go to Questions #1-6 about this section, then return to continue on to the next

section.

How do you solve 2 Step equations? Solving 2-Step Equations ☻ Solving equations is just a matter of undoing the operations that are being done to the variable. We already did 1-step equations… Example 1: Example 2: x – 3 = -9Operation Now: -5x = 30Operation Now:

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