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
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I'm Chandrajeet, an in-house writer for iCoachMath. iCoachMath is an effective, convenient, easy-to-use online Math Program which has been used by thousands of students, teachers, and parents. iCoachMath strives to lead K-12 students to excellence in math by offering quality web-based educational solutions. iCoachMath's instructional and lesson materials are aligned to State Curriculum Standards in all 50 states (USA).
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