Question

How do you solve $7x+4=3x+7?$

Answer 1

Hint: As the above equation is in the form of linear equation, in order to solve it we have to separate the like terms at one side, then by using BODMAS we will determine the value of unknown quantity “x”.

Complete step by step solution:
As per data given in the question,
As we have,
$7x+4=3x+7$
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,
$\Rightarrow 7x+4=3x+7$
Here, we will shift 3x from right side to left side and 4 from left side to right side,
We will get,
$\Rightarrow 7x-3x=7-4$
Now, using BODMAS, to solving the values,
We will get,
$4x=3$
As, here the value of$4x$ is $3$
So, for getting the value of $''x''$ we need to shift 4 from left side to right side,
As 4 is in multiplication with $''x'',$
So, when it will be shifted in right hand side, it will come in division,
Hence,
$4x=3$
$\Rightarrow x=\dfrac{3}{4}$
Hence,
Value of $''x''$in above given equation will be $\dfrac{3}{4}$
i.e. if we put $''x=\dfrac{3}{4}''$ 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 the right side, will be converted into a division.
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 arithmetical 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.