Question

Solve the given equation for x.
$\dfrac{4x+8}{5x+8}=\dfrac{5}{6}$

Answer 1

Hint: Here, in this question, we can cross multiply the numerator of the Left Hand Side (LHS) with the denominator of the Right Hand Side (RHS) and do the same with the numerator of the Right Hand Side (RHS) and the denominator of the Left Hand Side (LHS) and then equalize them. Then, we just need to simplify the linear equation in order to get the value of x.

Complete step-by-step answer:
In this given question, we are given the equation $\dfrac{4x+8}{5x+8}=\dfrac{5}{6}$ and asked to solve it for x.
The process of solving is as follows:
First of all we do the cross multiplication of the numerator and denominator of the Left Hand Side (LHS) with the denominator and the numerator Right Hand Side (RHS) respectively.
$\begin{align}
  & \dfrac{4x+8}{5x+8}=\dfrac{5}{6} \\
 & \Rightarrow \left( 4x+8 \right)\times 6=\left( 5x+8 \right)\times 5 \\
 & \Rightarrow 24x+48=25x+40..........(1.1) \\
\end{align}$
Now, solving equation 1.1 for x, we get,
$\begin{align}
  & 24x+48=25x+40 \\
 & \Rightarrow 25x-24x=48-40 \\
 & \Rightarrow x=8............(1.2) \\
\end{align}$
So, from equation 1.2, we get x is equal to 8.
Therefore, the required value of x is 8.

Note: In this sort of question, we must be careful while doing cross multiplication not to multiply numerator with numerator and denominator with denominator. If we do this, we will get wrong answers. We can also try taking 2 outside from the term (4x+8) and performing the cross multiplication, then simplifying further.