Question

How do you solve $3x + 2\left( {5x + 4} \right) = 47$?

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. To solve the equation first open the brackets then take all $x$ terms to one side and all constants to the others side and solve for required $x$.

Complete step by step solution:
Given equation is $3x + 2\left( {5x + 4} \right) = 47$, and we have to solve for $x$,
Now taking out the brackets we get,
$ \Rightarrow 3x + 10x + 8 = 47$,
Now simplifying we get,
$ \Rightarrow 13x + 8 = 47$,
Now subtract 8 from both sides of the equation, we get,
$ \Rightarrow 13x + 8 - 8 = 47 - 8$,
Now simplifying by eliminating the like terms, we get,
$ \Rightarrow 13x = 39$,
Now divide 13 to both sides of the equation we get,
$ \Rightarrow \dfrac{{13x}}{{13}} = \dfrac{{39}}{{13}}$,
Now simplifying we get,
$ \Rightarrow x = 3$,
So the value of $x$ will be 3, i.e., when we substitute the value of $x$ in the equation $3x + 2\left( {5x + 4} \right) = 47$, then right hand side of the equation will be equal to left hand side of the equation, we get,
$ \Rightarrow 3x + 2\left( {5x + 4} \right) = 47$,
Now substitute $x = 3$, we get,
$ \Rightarrow 3\left( 3 \right) + 2\left( {5\left( 3 \right) + 4} \right) = 47$,
Now simplifying we get,
$ \Rightarrow 9 + 2\left( {15 + 4} \right) = 47$ ,
Further simplifying we get,
$ \Rightarrow 9 + 2\left( {19} \right) = 47$,
Now multiplying we get,
$ \Rightarrow 9 + 38 = 47$,
Now simplifying we get,
$ \Rightarrow 47 = 47$
Therefore here R.H.S=L.H.S.
So, the value of $x$ is $3$.

$\therefore $ The value of $x$ when the equation $3x + 2\left( {5x + 4} \right) = 47$ is solved will be equal to $3$.

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.