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Addition Property of Equality

The Addition Property of Equality states that if the SAME number is added to both sides of an equation, the two sides remain equal.

In other words, we can always add the SAME quantity to both sides of an equation.

That is:

If x = y then x + z = y + z.

Example of Addition Property of Equality

Consider the equation 3 = 3.

The Addition Property of Equality allows us to add the same quantity to both sides of the equation.

3 + 2 = 3 + 2

5 = 5. It's true.

Consider another equation x – 4 = 3.

According to the Addition Property of Equality we can add 4 to both sides of the equation.

x – 4 + 4 = 3 + 4

x = 3 + 4 >> Observe that by adding 4 to each side, the variable ‘x’ has been isolated on one side.

x = 7

More about Addition Property of Equality

The Addition Property of Equality can also be stated as follows:

If x = y and a = b, then x + a = y + b.

It appears as though we are adding different quantities to both sides of the equation.

Keep in mind that we are given a = b. So, we're in fact adding the SAME quantity to both sides of the equation.

Addition Property of Inequality

The Addition Property of Inequality states that adding the SAME?number to both sides of an inequality does NOT affect the inequality.

That is,

If x > y, then x + z > y + z.

If x < y, then x + z < y + z.

Example of Addition Property of Inequality

Consider the inequality 3 > 2.

The Addition Property of Inequality allows us to add the same amount to both sides of the inequality.

3 + 4 > 2 + 4

7 > 6. It's true.

Let me help you understand.

Suppose you have 3 cookies and I have 2 cookies. If somebody gives each of us 4 cookies, then you’ll still have more cookies than I do.

Consider another inequality x – 3 < 5.

According to the Addition Property of Inequality we can add 3 to both sides of the inequality.

x – 3 + 3 < 5 + 3

x < 5 + 3 >>observe that by adding 3 to each side; the variable ‘x’ has been isolated on one side.

X < 8

More about Addition Property of Inequality

The following is another Addition Property of inequality.

If x < y and a < b, then x + a < y + b.

For Example:

4 < 5 and 2 < 3

4 + 2 < 5 + 3

6 < 8

Similarly,

If x > y and a > b, then x + a > y + b.

For Example:

7 > 6 and 2 > 1

7 + 2 > 6 + 1

9 > 7