EQUIVALENT EQUATIONS

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.