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?
- A. 3x = - 45
- B. 3x = 45
- C. 2x = 15 - x
- D. x + 3 = - 18
Correct Answer: A
- 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.