EQUIVALENT EQUATIONS

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 = 15Step 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.

Quick Summary

Equivalent equations have identical solutions.
Performing the same operation on both sides maintains equivalence.

\[ If \(f(x) = g(x)\) and \(g(x) = h(x)\), then \(f(x) = h(x)\) are equivalent. \]

🍎 Teacher Insights

Emphasize the importance of performing the same operation on both sides to maintain the equality.

🎓 Prerequisites

Solving linear equations
Simplifying expressions

Check Your Knowledge

Q1: Which equation is equivalent to x + 5 = 10?

A. x + 2 = 5 B. x - 5 = 0 C. 2x = 10 D. 3x = 15

Q2: Which equation is equivalent to 2x = 8?

A. x = 2 B. x + 2 = 6 C. x/2 = 4 D. x - 2 = 2

Frequently Asked Questions

Q: How can I check if two equations are equivalent?
A: Solve each equation and compare their solutions. If the solutions are the same, the equations are equivalent.

Q: Are all linear equations equivalent?
A: No, only equations with the same solution set are equivalent.