Question

Solve the given expression to obtain the value of x:
$\dfrac{{2x + 7}}{3} = \left( {x + 4} \right)$

Answer 1

Hint – In this question we need to solve for the value of x, use cross multiplication along with a simple simplification technique to solve the given equation for the value of x.

Complete step-by-step answer:
Given equation is
$\dfrac{{2x + 7}}{3} = \left( {x + 4} \right)$
Now the given equation is also written as
$\dfrac{{2x + 7}}{3} = \dfrac{{x + 4}}{1}$
Now apply cross multiplication method (i.e. (2x + 1) is multiplied by 1 and (x + 4) is multiplied by 3)
$ \Rightarrow 1\left( {2x + 7} \right) = 3\left( {x + 4} \right)$
Now simplify the above equation we have,
$ \Rightarrow 2x + 7 = 3x + 12$
Now shifting the variables i.e. 3x to L.H.S and 7 to R.H.S we have
$ \Rightarrow 2x - 3x = 12 - 7$
$ \Rightarrow - x = 5$
Now multiply by -1 we have,
$ \Rightarrow x = - 5$
So, this is the required solution of the given equation.
So, this is the required answer.

Note – Whenever we face such types of problems the key concept is simply to use basic techniques of cross multiplication and subtraction of terms with the same variables. This concept will help you get on the right track to reach the answer.