Question

How do you solve $3\left( 5m-7 \right)-2\left( 9m-11 \right)=4\left( 8m-13 \right)-17?$

Answer 1

Hint: As the above equation is in form of linear equation, in order to solving it first simplify the each individual terms by multiplying them, like $3\left( 5m-7 \right)=15m-21,$ similarly simplifying all the terms, and then by separating the like terms at one side of equation, determine the value of unknown quantity $''m''$.

Complete step-by-step solution:
As per data given in the question,
As we have,
$\Rightarrow 3(5m-7)-2(9m-11)=4(8m-13)-17$
Now,
Multiplying $3$ with $''5m''$ and $''-7''$
We will get,
$\Rightarrow 15m-21-2\left( 9m-11 \right)=4\left( 8m-13 \right)-17$
Now,
Multiplying $''-2''$ with $''9m''$ and $''-11''$
We will get,
$\Rightarrow 15m-21-18m+22=4\left( 8m-13 \right)-17$
Similarly,
The above equation can be rewritten as,
$\Rightarrow 15m-21-18m-22=32m-52-17$
Now separating the like terms, like shifting all the terms which consists $''m''$ and shifting all the remaining constants in the right side of equal to,
We will get,
$\Rightarrow 15m-18m-32m=-52-17-22+21$
Now, solving both side of equation,
We will get,
$\Rightarrow -35m=-70$
As, here both the side of equation consists of negative sign,
So, the negative sign of left-hand side get cancelled with negative sign of right-hand side,
So, we will get,
$\Rightarrow 35m=70$
Now, in above equation, as the value of $35m$ is $70$
So, for getting the value of $''m''$ we need to shift 35 from left side to right side,
As 35 is in multiplication with $''m'',$
So, when it will be shifted in right hand side, it will come in division,
Hence,
$\Rightarrow 35m=70$
So, \[m=\dfrac{70}{35}=2\]

Value of $''m''$ in above given equation will be $2.$

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 $2x=2-1$
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, $\dfrac{1}{2}x=5\Rightarrow x=\left( 5\times 2 \right)$

Note: 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, $2x=8\Rightarrow x=\dfrac{8}{2}=4$