transitive property
If a=b and b=c, then a=c; skip the middle man
The transitive property is a mathematical principle that states that if A equals B, and if B equals C, then A must also equal C. This property is used in many different areas of mathematics, including algebra, geometry, and calculus.
For example, if we have the equations 3x + 2 = 11 and 11 = 5x – 3, we can use the transitive property to solve for x. First, we can solve the first equation for x by subtracting 2 from both sides and dividing by 3, giving us x = 3. Then, we can substitute this value of x into the second equation, giving us 11 = 5(3) – 3. Simplifying this expression gives us 11 = 12 – 3, or 11 = 9. This result seems contradictory, but it simply means that there is no solution that satisfies both equations (in this case, the equations are inconsistent).
The transitive property is a fundamental principle of mathematics and is used in many different types of problems, including proofs of theorems and equations involving inequalities. It is essential for students of mathematics to understand this property and be able to use it effectively in their work.
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