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Transitive Property of Equality

The equality properties are used to activate, stable the equations. Generally, equality is referred as follows,

1. m = n indicates m is equal to n.
2. m $\neq$ n indicates m is not equal to n.

Thus, the properties of equalities contain the following properties.

Balance Equation Relation Property

2. Subtraction property
3. Multiplication property
4. Division property

Equivalence Relation Property

1. Reflexive property
2. Symmetric property
3. Transitive property

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Transitive Property of Equality Definition

The transitive property of equality for any real numbers a, b, and c is as follows. If a = b and b = c, then a = c. Generally, the transitive property deals with following categories:

1. Transitive Property of Equalities
2. Transitive Property of Inequalities

Transitive Property of Equalities:

If m, n, and o are real numbers, then transitive property of equalities states that if m = n and n = o, then m = o. Thus, the two quantities that are equal to the same quantity are identical to each other. Otherwise, transitive property of equalities is referred as, if two numericals are equal to the same number, then all numericals are equal to each other.

Transitive Property of Inequalities:

The transitive property of inequalities states as follow:

• If x < y and y < z, then x < z.
• If x $\leq$ y and y $\leq$ z, then x $\leq$ z.
• If x > y and y > z, then x > z.
• If x $\geq$ y and y $\geq$ z, then x $\geq$ z
Also, the transitive property of inequalities says that if a number is less than or equal to a second number, and the second number is less than or equal to a third number, then the first number is also less than or equal to the third number.

Transitive Property of Equality Examples

Given below are some of the examples of transitive property of equalities:

Solved Examples

Question 1: Solve for m using transitive property of equality in algebra of the expression. m - 4 = 7 and then 7 = 2 + 3m
Solution:

Given m - 4 = 7 and 7 = 2 + 3m

According to transitive property of equality in algebra, we can equate the given expression as

m - 4 = 2 + 3m

Find the value of m.

-4 - 2 = 3m - m

-6 = 2m

m = -3.

Question 2:

Pick the correct option using transitive property of the expression 8 > (4 + y) and (4 + y) > 5

1. 8 > (4 + y)
2. 8 < 5
3. 8 > 5
4. 8 > 4y

Solution:

According to the condition of transitive property of inequalities in algebra, a > b and b > c. So, we can say that a > c

a > b = 8 > (4 + y)

b > c = 4 + y > 5

a > c = 8 > 5

The correct answer is option 8 > 5

Question 3: Solve for x using transitive property of equality in algebra of the expression. X + 4 = 6 and then 6 = 2 + 2X
Solution:

Given X + 4 = 6 and 6 = 2 + 2X

According to transitive property of equality in algebra, we can equate the given expression as

X + 4 = 2 + 2X

Now, we can find the value of X.

X + 4 = 2 + 2X

2X - X = 4 - 2

X = 2

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