Question

5. Sara thinks the following expressions are equivalent:

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

Answer 1

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

`2x + 3≠ (x)/(2) + (3)/(4)`

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

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

`R. H. S = (x)/(2) + (3)/(4) \\ = (x * 2)/(2 * 2) + ( 3)/(4) \\ = (2x + 3)/(4)`

Clearly,

`2x + 3≠ (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

`(2x + 3)/(4) = (2x + 3)/(4) \\ ๛L.H.S.=R. H. S`

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