Question

How do you solve $ 4 + 5\left( {7x - 3} \right) = 9\left( {x - 5} \right) $ ?

Answer 1

Hint: In this question we have to solve the equation for \[x\] , the given equation is a linear equation as the degree of the highest exponent of \[x\] is equal to 1. First we have to multiply the numbers and the binomial and next 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 $4 + 5\left( {7x - 3} \right) = 9\left( {x - 5} \right)$, and we have to solve for \[x\],
Given equation is a linear equation as the highest degree of \[x\] will be equal to 1,
$ \Rightarrow 4 + 5\left( {7x - 3} \right) = 9\left( {x - 5} \right)$,
Now multiply the numbers and the binomial, we get,
$ \Rightarrow 4 + 35x - 15 = 9x - 45$,
Now simplifying we get,
$ \Rightarrow 35x - 11 = 9x - 45$
Now transform the equation by taking all \[x\] terms to one side and all constants to the other side we get,
$ \Rightarrow 35x - 9x = - 45 + 11$,
Now simplifying we get,
$ \Rightarrow 26x = - 34$
Now divide both sides with 26, we get,
\[ \Rightarrow \dfrac{{26x}}{{26}} = \dfrac{{ - 34}}{{26}}\],
Now simplifying we get,
\[ \Rightarrow x = \dfrac{{ - 17}}{{13}}\],
So the value of \[x\] will be$\dfrac{{ - 17}}{{13}}$, i.e., when we substitute the value of\[x\]in the equation$4 + 5\left( {7x - 3} \right) = 9\left( {x - 5} \right)$, then right hand side of the equation will be equal to left hand side of the equation, we get,
$ \Rightarrow $$4 + 5\left( {7x - 3} \right) = 9\left( {x - 5} \right)$,
Now substitute\[x = \dfrac{{ - 17}}{{13}}\], we get,
\[ \Rightarrow 4 + 5\left( {7\left( {\dfrac{{ - 17}}{{13}}} \right) - 3} \right) = 9\left( {\left( {\dfrac{{ - 17}}{{13}}} \right) - 5} \right)\],
Now simplifying by taking L.C.M, we get,
\[ \Rightarrow 4 + 5\left( {\left( {\dfrac{{ - 117 - 39}}{{13}}} \right)} \right) = 9\left( {\dfrac{{ - 17 - 65}}{{13}}} \right)\],
Now simplifying we get,
\[ \Rightarrow 4 + 5\left( {\left( {\dfrac{{ - 156}}{{13}}} \right)} \right) = 9\left( {\dfrac{{ - 82}}{{13}}} \right)\],
Again taking L.C.M on the right hand side we get,
\[ \Rightarrow \dfrac{{4 \times 13 - 780}}{{13}} = \dfrac{{ - 738}}{{13}}\],
Now multiplying the numbers we get,
\[ \Rightarrow \dfrac{{52 - 780}}{{13}} = \dfrac{{ - 738}}{{13}}\],
Further simplifying we get,
\[ \Rightarrow \dfrac{{ - 738}}{{13}} = \dfrac{{ - 738}}{{13}}\],
So R.H.S=L.H.S.

The value of \[x\] when the equation $ 4 + 5\left( {7x - 3} \right) = 9\left( {x - 5} \right) $ is solved will be equal to $ \dfrac{{ - 17}}{{13}} $ .

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.