Answer
Verified
408.9k+ views
Hint:The key for solving this problem easily is to isolate P as we need to find the value of P in the given equation. The elimination method can be used for solving systems of linear equations and to solve the value for P here we can add the same value to each side of the equation while keeping the equation balanced.
Complete step by step solution:
In order to isolate the term containing \[P\] while keeping the equation balanced, we need to subtract \[B\] from each side of the equation.
\[
\Rightarrow S - B = - B + B + \left( {\dfrac{1}{2}} \right)Pl \\
\Rightarrow S - B = 0 + \left( {\dfrac{1}{2}} \right)Pl \\
\Rightarrow S - B = \left( {\dfrac{1}{2}} \right)Pl \\
\]
Now we need to multiply both the sides of equations by 2 for eliminating the fraction by keeping the equation balanced
\[
\Rightarrow 2(S - B) = 2 \times \left( {\dfrac{1}{2}} \right)Pl \\
\Rightarrow 2(S - B) = Pl \\
\]
To solve for \[P\] we need to divide each side of the equation by \[l\] while keeping the equation balanced
\[
\Rightarrow \dfrac{{2(S - B)}}{l} = \dfrac{{Pl}}{l} \\
\Rightarrow \dfrac{{2(S - B)}}{l} = P \\
\Rightarrow P = \dfrac{{2(S - B)}}{l} \\
\]
So the value for \[P\] comes out to be \[\dfrac{{2(S - B)}}{l}\] which means option A is correct.
Additional Information: To solve this problem in a better way it is important to simplify each side of the equation by removing parentheses and combining like terms. Addition or subtraction is used to isolate variable terms on one side of the equation while to solve the variable multiplication or subtraction is used.
Notes: Remember we need to isolate the variable by dividing each side by factor that is not containing the variable. The value of \[P\] can further be written in more simplified way as
\[P = \left( {\dfrac{{2S}}{l}} \right) - \left( {\dfrac{{2B}}{l}} \right)\]
We can remove fractions by multiplying each side of the equation with the common denominator. Remember that the solution of the linear equation is not affected if the same number is added or subtracted from both sides of the equation and if both the sides of the equation is multiplied or divided by the same non-zero number.
Complete step by step solution:
In order to isolate the term containing \[P\] while keeping the equation balanced, we need to subtract \[B\] from each side of the equation.
\[
\Rightarrow S - B = - B + B + \left( {\dfrac{1}{2}} \right)Pl \\
\Rightarrow S - B = 0 + \left( {\dfrac{1}{2}} \right)Pl \\
\Rightarrow S - B = \left( {\dfrac{1}{2}} \right)Pl \\
\]
Now we need to multiply both the sides of equations by 2 for eliminating the fraction by keeping the equation balanced
\[
\Rightarrow 2(S - B) = 2 \times \left( {\dfrac{1}{2}} \right)Pl \\
\Rightarrow 2(S - B) = Pl \\
\]
To solve for \[P\] we need to divide each side of the equation by \[l\] while keeping the equation balanced
\[
\Rightarrow \dfrac{{2(S - B)}}{l} = \dfrac{{Pl}}{l} \\
\Rightarrow \dfrac{{2(S - B)}}{l} = P \\
\Rightarrow P = \dfrac{{2(S - B)}}{l} \\
\]
So the value for \[P\] comes out to be \[\dfrac{{2(S - B)}}{l}\] which means option A is correct.
Additional Information: To solve this problem in a better way it is important to simplify each side of the equation by removing parentheses and combining like terms. Addition or subtraction is used to isolate variable terms on one side of the equation while to solve the variable multiplication or subtraction is used.
Notes: Remember we need to isolate the variable by dividing each side by factor that is not containing the variable. The value of \[P\] can further be written in more simplified way as
\[P = \left( {\dfrac{{2S}}{l}} \right) - \left( {\dfrac{{2B}}{l}} \right)\]
We can remove fractions by multiplying each side of the equation with the common denominator. Remember that the solution of the linear equation is not affected if the same number is added or subtracted from both sides of the equation and if both the sides of the equation is multiplied or divided by the same non-zero number.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE