**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

32*a*= 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 givesx= - 15.

Step 9:So, the equation equivalent to the given equation is 3x= - 45.

**Related Terms for Equivalent Equations**

- Solution
- Equation