Question

How do you solve $2x+3=11?$

Answer 1

Hint: The above given equation is type of linear equation, in order to solve the value of $'x'$, first separate the like terms i.e. $3$ from left hand side to right hand side and by using the Rule of BODMAS determine the value of $'x'$

Complete step-by-step answer:
As per data given in the question,
We have to determine the value of $'x'$
As above equation is,
$2x+3=11$
Here, we can easily solve the expression by separating the like terms,
So, in order to solving the equation,
Moving $+3$ from left side to right side,
We will get,
$2x+3=11$
$\Rightarrow 2x=11-3$
$\Rightarrow 2x=8$
As, the value of $2x$ is $8,$
So, we can easily determine the value of $x,$
Value of $x$ will be,
$2x=8$
$\Rightarrow x=\dfrac{8}{2}=4$

Hence, the value of $'x'$ in the given equation, $2x+3=11$ will be $4$.

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 $+1$ gets converted into negative sign.
Thus, it will equal to $2x=2-1$
Similarly, in $2-3x=-4,$ If here we more $-3x$ 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 $x=5,$ 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.
$2x\times 3=11$
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. Will subtract $3$ from side,
So, equation becomes,
$2x+3-3=11-3$
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.