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 Question from mario, a student: The area of a rectangle when on side is x and the other is x+6

Hi Mario,

Suppose $x = 2$ so that one side is of length 2 units. How long is the other side? What is the area? Do it!

Suppose $x = 4$ so that one side is of length 4 units. How long is the other side? What is the area? Do it!

In the first case you added 2 to 6 to get $2 + 6 = 8$ and then you multiplied the one dimension, 2 units, by the second dimension, 8 units. to find the area in square units. In the second case you also added $x$ to 6 to find the second dimension and then multiplied the two dimension to obtain the area.

To say this algebraically you need to be able to say "Add the value of $x$ to 6 to find the second dimension and then multiply the two dimensions to obtain the area." We use parentheses to make this clear. Putting $x + 6$ in parentheses, $(x + 6),$ tells me to add $x$ and 6 first. Now multiply this by $x$ to obtain the area in square units.

I hope this helps,
Harley

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