Question

How do you solve $\left[ \dfrac{\left( 3x-1 \right)}{\left( 5x-4 \right)} \right]=4$

Answer 1

Hint: As the above equation is in form of linear equation, in order to solving it first multiply $\left( 5x-4 \right)$ with$4$ as, $\left( 5x-4 \right)$ is in division in left side so when it will shifted in right side then it will comes in multiplication, then by separating the like terms, determine the value of $''x''.$.

Complete step by step solution:
As per data given in the question,
As we have
$\left[ \dfrac{\left( 3x-1 \right)}{\left( 5x-4 \right)} \right]=4$
Now,
Multiplying $\left( 5x-4 \right)$ with $4$
As, $\left( 5x-4 \right)$ is in division in left side, so when it will be shifted in right side it will comes in multiplication,
So,
We will get,
$\Rightarrow 3x-1=(5x-4)\times 4$
$\Rightarrow 3x-1=20x-16$
Now separating the like terms, like shifting all the terms which consists “x” and shifting all the remaining constants in the right side of equal to,
We will get,
$\Rightarrow 3x-20x=-16+1$
$\Rightarrow -17x=-15$
Now, in above equation, as the value of $-17x=-15$
So, for getting the value of “x” we need to shift $\left( -17 \right)$ from left side to right side,
As $\left( -17 \right)$ is in multiplication with $''x'',$
So, when it will be shifted in right hand side, it will come in division,
Hence,
$\Rightarrow -17x=-15$
As here in both side negative sign is present,
So the negative sign from both side get cancelled,
So,
We will get,
$\Rightarrow 17x=15$
$x=\dfrac{15}{17}$
Hence,
Value of $''x''$in above given equation will be$\dfrac{15}{17}$
i.e. if we put $x=\dfrac{15}{17}$ in the equation given in the question, then the value of the left-hand side will be equal to the value of the right-hand side.

Additional information:.
When we move any mathematical expression from left to right side or vice versa then the sign of the expression gets reversed.
Like, $2x+1=2,$ if we move $1$ from left side to right side i.e. after equal to then the positive sign of $+1$ get converted into negative sign,
Thus, it will equal to $2x=2-1$
Similarly, in $2-3x=-4$, if here we move $-3x$ from left side to right side then it will become positive, and if we move $-4$ from right side to left side it will become $+4.$
So, $2-3x=-4\Rightarrow 3x=2+4$
Similarly, if $2x=4,$ then here $2$ is in multiplication with x, in order to determine the value of x we have to replace 2 from left side to right side, so it will become divided.
i.e. $2x=4\Rightarrow x=\dfrac{4}{2},$ here, $2$ which are in multiplication on the left side, when transferred to right side, will be converted into divide.
In the same way, if $\dfrac{1}{2}x=5,$ here $2$ is in division with x on the left side, so when we solve the equation then it will be transferred to the right side, and converted into multiplication.
Like,$\dfrac{1}{2}x=5\Rightarrow x=\left( 5\times 2 \right)$
There are two ways to solve the equation of linear equation,
(1) By separating the like terms, like terms are those numbers which are similar in nature, like, $\left( 2x,\dfrac{1}{2}x,3x \right)$ or any constant.
(2) By adding or subtracting or by doing arithmetic processes.
Like if we have to solve,
$\Rightarrow 2x+3=11$
Here, as we have to determine the value of $2x,$
As 3 is in addition with $2x$ in left side,
So, in order to neutralise it,
We will subtract $3$ from both side,
So, equation becomes,
$\Rightarrow 2x+3-3=11-3$
$\Rightarrow 2x=8$
Now, we can solve the value of x,
As, $2x=8\Rightarrow x=\dfrac{8}{2}=4$

Note: While transferring the digits or constants or any variables or numbers from left hand side to right hand side, make sure you are reversing its symbol.
For any mathematical operation, always follow only the BODMAS rule.