matthew094
Answered

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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?​

Sagot :

[tex]\sf\purple{No, \:Sara\: is \:wrong.}[/tex]

[tex]2x + 3≠ \frac{x}{2} + \frac{3}{4} [/tex]

[tex]\sf\red{Here's\:why:}[/tex]

[tex]L. H. S. = 2x + 3[/tex]

[tex]R. H. S = \frac{x}{2} + \frac{3}{4} \\ = \frac{x \times 2}{2 \times 2} + \frac{ 3}{4} \\ = \frac{2x + 3}{4} [/tex]

Clearly,

[tex]2x + 3≠ \frac{2x + 3}{4} \\✒ \: L.H.S.\:≠\:R. H. S. [/tex]

[tex]\boxed{Therefore,\:the\:two\:expressions \:are\:not\:equivalent.}[/tex]

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

By doing so, she'll have

[tex] \frac{2x + 3}{4} = \frac{2x + 3}{4} \\ ๛L.H.S.=R. H. S[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

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