Question

Solve
\[\dfrac{7}{4} - p = 11\]

Answer 1

Hint: In the given problem we need to solve this for ‘p’. We can solve this using the transposition method. The common transposition method is to do the same thing (mathematically) to both sides of the equation to bring like terms together and isolate the variable (or the unknown quantity). That is we group the ‘p’ terms on one side and constants on the other side of the equation.

Complete step-by-step answer:
Given, \[\dfrac{7}{4} - p = 11\].
We transpose ‘-p’ which is present in the left hand side of the equation to the right hand side of the equation by adding ‘p’ on the right hand side of the equation.
\[\dfrac{7}{4} = 11 + p\]
Or
\[11 + p = \dfrac{7}{4}\]
Similarly we transpose 11 to the right hand side of the equation by subtracting 11 on the right hand side of the equation.
\[p = \dfrac{7}{4} - 11\]
\[p = \dfrac{{7 - 44}}{4}\]
\[ \Rightarrow p = \dfrac{{ - 37}}{4}\]. This is the exact form.
\[ \Rightarrow p = 9.25\].This is the decimal form.

Note: We can check whether the obtained solution is correct or wrong. All we need to do is substituting the value of ‘p’ in the given problem.
\[\dfrac{7}{4} - \left( {\dfrac{{ - 37}}{4}} \right) = 11\]
\[\dfrac{7}{4} + \dfrac{{37}}{4} = 11\]
\[\dfrac{{7 + 37}}{4} = 11\]
\[\dfrac{{44}}{4} = 11\]
Simplifying we have,
\[ \Rightarrow 11 = 11\].
That is LHS=RHS. Hence the obtained is correct.
In the above we did the transpose of addition and subtraction. Similarly, if we have multiplication we use division to transpose. If we have division, we use multiplication to transpose. Follow the same procedure for these kinds of problems.