﻿ Definition and examples equivalent expression | define equivalent expression - algebra - Free Math Dictionary Online

# 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

### 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

### 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.

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