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#### Equivalent Equations

Definition of Equivalent Equations

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

### Examples of Equivalent Equations

• The following are 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

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: Among the choices listed, 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