Question

Solve the linear equation \[\dfrac{5x-4}{8}-\dfrac{x-3}{5}=\dfrac{x+6}{4}\]
A.9
B.8
C.7
D.6

Answer 1

Hint: To solve this kind of questions, we need to know about basic concepts like fractions. The given problem is simplified by step-by-step method to find out the value of x. First, we need to find out the LCM of the denominator and after that solve the simplified form to find out the value of x.

Complete step-by-step solution:
Fraction is defined as it represents any number with equal parts in a set of whole numbers. It is represented in the form of ‘/’, for example a/b. The number on the top is known as ‘numerator’, and the number below is called ‘denominator’. There are 6 different types of fractions namely proper fractions, improper, like, unlike and mixed fractions.
Let us solve the given question,
Here the given question is \[\dfrac{5x-4}{8}-\dfrac{x-3}{5}=\dfrac{x+6}{4}\]
We have the question in the fraction form,
Firstly, we need to find the L.C.M of the denominators of 8,5,4
\[\begin{align}
  & 8=2\times 2\times 2 \\
 & 5=1\times 5 \\
 & 4=2\times 2 \\
\end{align}\]
From above, the LCM of \[8,5,4=2\times 2\times 5\times 2=40\]
The LCM of 8,5,4 is 40.
We can simplify the given question as,
\[\Rightarrow \dfrac{5\left( 5x-4 \right)-8\left( x-3 \right)}{40}=\dfrac{x+6}{4}\]
By cancelling the terms, we get
 \[\Rightarrow 5\left( 5x-4 \right)-8\left( x-3 \right)=10\left( x+6 \right)\]
Multiplying the terms individually, then
 \[\Rightarrow 25x-20-8x+24=10x+60\]
Separating the x coefficient terms and constants,
\[\Rightarrow 25x-8x-10x=60-24+20\]
On simplifying,
 \[\begin{align}
  & \Rightarrow 7x=56 \\
 & \Rightarrow x=\dfrac{56}{7} \\
 & \therefore x=8. \\
\end{align}\]
The value of x is 8.
The correct answer is (B).

Note: The common mistake done in fractions concept is believing that fractions’ numerators and denominators should be managed as a set of whole numbers. Most of the mistakes happen here. Students leave the denominator unchanged in fraction multiplication problems. And also failing to understand the reciprocate-and multiply procedure for solving fraction-based division problems.