Question

How do you solve $2f\left( {5f - 2} \right) - 10\left( {{f^2} - 3f + 6} \right) = - 8f\left( {f + 4} \right) + 4\left( {2{f^2} - 7f} \right)$?

Answer 1

Hint: In this question we have to solve the equation for\[f\], for this we will open the brackets and then after simplifying the given equation, then the equation will become a linear equation with the degree of the highest exponent of \[x\] is equal to 1. To solve the equation take all \[x\] terms to one side and all constants to the other side and solve for required \[x\].

Complete step by step answer:
Given equation is $2f\left( {5f - 2} \right) - 10\left( {{f^2} - 3f + 6} \right) = - 8f\left( {f + 4} \right) + 4\left( {2{f^2} - 7f} \right)$, and we have to solve for \[f\],
Now transform the given equation by opening the brackets, i.e.,
$ \Rightarrow 10{f^2} - 4f - 10{f^2} + 30f - 60 = - 8{f^2} - 32f + 8{f^2} - 28f$,
Now simplifying the equation by eliminating the like terms we get,
$ \Rightarrow - 4f + 30f - 60 = - 32f - 28f$,
Now simplifying the equation we get,
$ \Rightarrow 26f - 60 = - 60f$,
Now we got an equation which is is a linear equation as the highest degree of\[x\]will be equal to 1,
Now adding 60 to both sides of the equation, we get,
$ \Rightarrow 26f - 60 + 60 = - 60f + 60$,
Now simplifying we get,
$ \Rightarrow 26f = - 60f + 60$,
Now add 60f to both sides we get,
\[ \Rightarrow 26f + 60f = - 60f + 60 + 60f\],
Now simplifying we get,
\[ \Rightarrow 86f = 60\],
Now divide both sides with 96 we get,
\[ \Rightarrow \dfrac{{86f}}{{86}} = \dfrac{{60}}{{86}}\],
Now simplifying we get,
\[ \Rightarrow f = \dfrac{{30}}{{43}}\],
So, the value of \[f\] is \[\dfrac{{30}}{{43}}\].

\[\therefore \]The value of \[f\] when the equation $2f\left( {5f - 2} \right) - 10\left( {{f^2} - 3f + 6} \right) = - 8f\left( {f + 4} \right) + 4\left( {2{f^2} - 7f} \right)$ is solved will be equal to \[\dfrac{{30}}{{43}}\].

Note:
A linear equation is an equation of a straight line having a maximum of one variable. The degree of the variable will be equal to 1. To solve any equation in one variable, pit all the variable terms on the left hand side and all the numerical values on the right hand side to make the calculation solved easily.