Video: Finding a Value of an Unknown in Algebraic Equations Using the Associative Property

If (π‘₯ + 55) + 32 = 24 + (55 + 32), what is the value of π‘₯?

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Video Transcript

If π‘₯ plus 55 plus 32 is equal to 24 plus 55 plus 32, what is the value of π‘₯?

In order to answer this question, we need to recall the associative property of addition. This states that the sum does not change, irrespective of how the numbers are grouped. For example, adding π‘Ž and 𝑏 and then adding 𝑐 to their sum is the same as adding 𝑏 and 𝑐 first and then adding π‘Ž to their sum.

In our case, we notice that we have a 55 on the left- and right-hand side of the equation. We also have a 32 on the right- and left-hand side of the equation. This means that the left-hand side, π‘₯ plus 55 inside the parentheses plus 32, can be rewritten with 55 and 32 inside the parentheses and π‘₯ outside.

We’re told that this is equal to 24 plus 55 plus 32. The 55 plus 32, or 87 if we add them, can be cancelled on both sides. This leaves us with π‘₯ is equal to 24. If π‘₯ plus 55 plus 32 is equal to 24 plus 55 plus 32, then π‘₯ is equal to 24.

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