Question

5. Sara thinks the following expressions are equivalent:

Answer 1

$\sf\purple{No, \:Sara\: is \:wrong.}$

$2x + 3≠ \frac{x}{2} + \frac{3}{4}$

$\sf\red{Here's\:why:}$

$L. H. S. = 2x + 3$

$R. H. S = \frac{x}{2} + \frac{3}{4} \\ = \frac{x \times 2}{2 \times 2} + \frac{ 3}{4} \\ = \frac{2x + 3}{4}$

Clearly,

$2x + 3≠ \frac{2x + 3}{4} \\✒ \: L.H.S.\:≠\:R. H. S.$

$\boxed{Therefore,\:the\:two\:expressions \:are\:not\:equivalent.}$

To make them equivalent, Sara can simply divide L. H. S. by 4.

By doing so, she'll have

$\frac{2x + 3}{4} = \frac{2x + 3}{4} \\ ๛L.H.S.=R. H. S$

$\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}$