Question

How do you solve $3p-1=5\left( p-1 \right)-2\left( 7-2p \right)?$

Answer 1

Hint: As the above equation is in form of linear equation, in order to solving it we have to separate the like terms at one side, then by using BODMAS we will determine the value of unknown quantity $''p''$
Multiplying $5$ with $\left( p-1 \right)$ and $2$ with $\left( 7-2p \right)$ then separate the like terms, and solve the value of unknown quantity $''p''$

Complete step-by-step solution:
As per data given in the question,
As we have,
$\Rightarrow 3p-1=5\left( p-1 \right)-2\left( 7-2p \right)$
Now multiplying $5$ with $\left( p-1 \right)$ and $2$ with $\left( 7-2p \right)$
We will get,
\[\Rightarrow 3p-1=5p-5-14+4p\]
Now for solving the value of $''p''$ separate the like terms at one side,
Means, shift all terms consists of $''p''$ from right side of equation to the left side of equation,
As we know that, when we shift any positive term from right side to the left side of equation, then the sign of the constant/variable get changed,
So,
\[\Rightarrow 3p-1=5p-5-14+4p\]
$\Rightarrow 3p-5p-4p = -5-14+1$
\[\Rightarrow -6p=-18\]
As here we can analyse that,
Both side of the equation consists of negative sign,
So, the negative of left side get cancelled by negative sign of right side,
So, we will get,
$6p=18$
As. Here the value of $6p$ is $18$
As here 6 is in multiplication with $''p''$ so for calculating the value of $''p''$ we need to shift $6$ from the left side of the equation to the right side of the equation.
As, here 6 is in multiplication with $''p''$, so when it is shifted in the right side of the equation it will come in division.
So,
$\Rightarrow p=\dfrac{18}{6}=3$

Hence, Value of $''p''$ in above given equation will be $3$

Note: 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, $2-3x=-4\Rightarrow 3x=2+4$