Question

Sarah thinks that the following expressions are equivalent: 2x+3=x/2+3/4 . Is she right? If so, prove that the two expressions are equivalent. If not, what error(s) did she make?

Answer 1

No, 2x + 3 ≠ x/2 + 3/4.

2x + 3 = 2(x/2 + 3/2)

Answer 2

not equivalent; one is 1/4 of the other

Explanation:

You want to know if the expressions (2x +3) and (x/2 +3/4) are equivalent, and why or why not.

Equivalence

The two expressions are equivalent if they have the same value for all values of x. When we let x=0, the values of these expressions are ...

2x +3 = 2·0 +3 = 3

x/2 +3/4 = 0/2 +3/4 = 3/4

Since 3 ≠ 3/4, the two expressions are not equivalent for every value of x, hence are not equivalent.

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