equivalent equations


Definition of Equivalent Equations

  • Equivalent Equations are the equations that have the same solution.

Examples of Equivalent Equations

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

Solved Example on Equivalent Equations

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.

Related Terms for Equivalent Equations

  • Solution
  • Equation