# Equivalent Equations

Let’s begin with the definition of equivalent equations.

We speak of “Equivalent Equations” when we have two (2) equations that are having the same solution set.

Question 1 of 2

1. Are the equations x = 4 and x + 8 = 3 equivalent?

A.
B.

Question 1 of 2

Question 2 of 2

2. Are the equations x = 64 and x - 34 = 30 equivalent?

A.
B.

Question 2 of 2

Next Lesson: Operations that Produce Equivalent Equations
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The transcript of the video is for your convenience. For example: Are the equations x = 7 and x + 2 = 9 equivalent? The solution: Our number 7 is the single possible solution of the equation x + 2 = 9. Similarly, the number 7 is the only solution to this equation: x = 7. Therefore we can say that x = 7 and x+2 = 9 have identical solution sets, so they are equivalent.

Another example: Are the equations x = 1 and x2 = x equivalent?

The solution: If we inspect this, the equation x2 = x has two solutions, 0 and 1.

On the other hand, our equation x = 1 has just a single solution, namely 1.

Hence, the equations x2 = x and x = 1 do not have the same solution sets and are not equivalent.

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