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Equivalent Equations

Definition of Equivalent Equations

Equivalent Equations are the equations that have the same solution.

Example of Equivalent Equations

The following are a few examples of equivalent equations.
x - 6 = 5 and x - 11 = 0
32a = 8 and a/4=1/8


Video Examples:Equivalent Equations: Methods Of Solving Equations


Solved Example on Equivalent Equations

Ques: Which of the following equations is equivalent to the equation 3(x � 5) = 4x?

Choices:
  • A. 3x = - 45
  • B. 3x = 45
  • C. 2x = 15 - x
  • D. x + 3 = - 18

Correct Answer: A

Solution:

  • Step 1: Let us first solve the equation 3(x � 5) = 4x.
  • Step 2: 3x � 15 = 4x [Simplify.]
  • Step 3: 3x � 4x = 15
  • Step 4: - x = 15
  • Step 5: x = - 15
  • Step 6: The solution is � 15.
  • Step 7: Now, we need to identify from the choices listed, the equation with the same solution, - 15.
  • Step 8: Out of the given choices, only 3x = - 45 gives x = - 15.
  • Step 9: So, the equation equivalent to the given equation is 3x = - 45.

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