Answer:
Given expression : [tex]\frac{9}{4}-2(4x+\frac{4}{3} )+\frac{5}{2}x[/tex] ......[1]
Using distributive property: [tex]a\cdot (b+c) =a\cdot b + a\cdot c[/tex]
[1]⇒ [tex]\frac{9}{4} - 2(4x) - 2(\frac{4}{3})+\frac{5}{2} x[/tex]
Simplify:
[tex]\frac{9}{4} - 8x - \frac{8}{3}+\frac{5}{2}x[/tex]
Like terms are those terms which are same variables.
Combine like terms: we get;
[tex](\frac{9}{4} - \frac{8}{3}) - 8x + \frac{5}{2}x[/tex] ......[2]
[tex]\frac{27-32}{12} -8x +\frac{5}{2} x[/tex]
Simplify:
[tex]\frac{-5}{12} -8x +\frac{5}{2}x[/tex]
or
[tex]\frac{-5}{12} - \frac{11}{2}x[/tex]
we can write equation [2] as;
[tex]\frac{27}{12} - \frac{8}{3} - 8x + \frac{5}{2}x[/tex]
Combine like terms of x variables;
[tex]\frac{27}{12} - \frac{8}{3} - \frac{11}{2}x[/tex]
Therefore, the expressions which are equivalent to the Given expression are:
[tex]\frac{9}{4} - 2(4x) - 2(\frac{4}{3})+\frac{5}{2} x[/tex]
[tex]\frac{-5}{12} -8x +\frac{5}{2}x[/tex]
[tex]\frac{27}{12} - \frac{8}{3} - \frac{11}{2}x[/tex]
[tex]\frac{-11}{2}x - \frac{5}{2}[/tex]
