# 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.

Translate :