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.

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

A.
B.

Question 1 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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