Question

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Answer 1

Answer:

Given expression : $\frac{9}{4}-2(4x+\frac{4}{3} )+\frac{5}{2}x$    ......[1]

Using distributive property:  $a\cdot (b+c) =a\cdot b + a\cdot c$

[1]⇒   $\frac{9}{4} - 2(4x) - 2(\frac{4}{3})+\frac{5}{2} x$

Simplify:

$\frac{9}{4} - 8x - \frac{8}{3}+\frac{5}{2}x$

Like terms are those terms which are same variables.

Combine like terms: we get;

$(\frac{9}{4} - \frac{8}{3}) - 8x + \frac{5}{2}x$            ......[2]

$\frac{27-32}{12} -8x +\frac{5}{2} x$

Simplify:

$\frac{-5}{12} -8x +\frac{5}{2}x$  

or

$\frac{-5}{12} - \frac{11}{2}x$  

we can write equation [2] as;

$\frac{27}{12} - \frac{8}{3} - 8x + \frac{5}{2}x$

Combine like terms of x variables;

$\frac{27}{12} - \frac{8}{3} - \frac{11}{2}x$

Therefore, the expressions which are equivalent to the Given expression are:

$\frac{9}{4} - 2(4x) - 2(\frac{4}{3})+\frac{5}{2} x$

$\frac{-5}{12} -8x +\frac{5}{2}x$  

$\frac{27}{12} - \frac{8}{3} - \frac{11}{2}x$

$\frac{-11}{2}x - \frac{5}{2}$