Math CentralQuandaries & Queries


Question from Francisco:

Solve for y: 2(x+3)=y x=5
Solve for y: (x+3)2=y x=5
Are those two equations the same?


I would use the commutative law for multiplication of the real numbers to solve this. The commutative law says that for any real numbers $a$ and $b, a \times b = b \times a.$ For your question if you let $a = 2$ and $b = x + 3,$ then by the commutative law

\[2 \times (x + 3) = (x + 3) \times 2.\]

hence by the commutative law

\[2(x + 3) = y \mbox{ and } (x + 3)2 = y\]

are two ways to write the same equation.


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