Question

Sarah thinks that the following expressions are equivalent: 2x + 3 = x/2+ ¾ Is she right? If so, prove that these two expressions are equivalent. If not, what error(s) did she make?

Answer 1

Solution:

Given that Sarah thinks;

$2x+3=\frac{x}{2}+\frac{3}{4}$

ANSWER: The two expressions are not equivalent because;

$\frac{x}{2}+\frac{3}{4}=\frac{1}{4}(2x+3)$

That is, 1/4 of the expression on the left side is on the right side.

Another Method

Let x =2, then substitute;

$\begin{gathered} 2x+3=2(2)+3 \\ \\ 2x+3=4+3 \\ \\ 2x+3=7 \end{gathered}$

Then, substitute in the second expression too;

$\begin{gathered} \frac{x}{2}+\frac{3}{4}=\frac{2}{2}+\frac{3}{4} \\ \\ \frac{x}{2}+\frac{3}{4}=1+\frac{3}{4} \\ \\ \frac{x}{2}+\frac{3}{4}=\frac{7}{4} \end{gathered}$

Since, the answers are not the same, then, the expressions are not equivalent.