# EQUIVALENT EQUATIONS

## Related Words

## 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 are equivalent as their solution is x = 11

16a = 8 and a / 4 = 1 / 8 are equivalent as their solution is a = 1/2

### Video Examples: Equivalent Equations

### Solved Examples on Equivalent Equations

**Ques:** Equations (x-5) / 3 = 2x / 5 and 2x + 1 5= -35 are equivalent.

##### Choices:

A. True

B. False

Correct Answer: A

**Solution:**

Step 1: (x-5)/3=2x/5 and 2x+15= -35 [Given equations.]

Step 2: 5(x-5)=3(2x) ? 5x-25 = 6x ? x= -25 [Solving the first equation.]

Step 3: 2x + 15 = -35 ?2x= -50 ? x = -25 [Solving the second equation.]

Step5: So, the two equations, (x-5)/3=2x/5 and 2x+15= -35 are equivalent.

**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 the equation with the same solution, -15 from the given choices.

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.