Question

How do you solve \[\dfrac{1}{2}m - \dfrac{3}{4}n = 16\], when \[n = 8\].?

Answer 1

Hint: In the given problem we need to solve this for ‘m’. We can solve this using the transposition method. Here we have two variables, one is ‘m’ and the other is ‘n’. We have the value of ‘n’. First we solve for ‘m’ then we substitute the given value of ‘n’ to get the value of ‘m’.

Complete step by step answer:
Given \[\dfrac{1}{2}m - \dfrac{3}{4}n = 16\].
Let’s solve for ‘m’
We transpose \[ - \dfrac{3}{4}n\] which is in the left side of the equation to right hand side of the equation by adding \[\dfrac{3}{4}n\] to the right hand side of the equation.
\[ \Rightarrow \dfrac{1}{2}m = 16 + \dfrac{3}{4}n\]
We transpose \[2\] to the right hand side of the equation by multiplying \[2\] to the right hand side of the equation.
\[ \Rightarrow m = 2\left( {16 + \dfrac{3}{4}n} \right)\]
Thus we have solved for ‘m’.
Now substitute the value of ‘n’ in the above equation.
\[ \Rightarrow m = 2\left( {16 + \dfrac{3}{4}n} \right)\], put \[n = 8\]. Then we have,
\[ \Rightarrow m = 2\left( {16 + \dfrac{3}{4} \times 8} \right)\]
\[ \Rightarrow m = 2\left( {16 + \left( {3 \times 2} \right)} \right)\]
\[ \Rightarrow m = 2\left( {16 + 6} \right)\]
\[ \Rightarrow m = 2\left( {22} \right)\]
\[ \Rightarrow m = 44\], is the required answer.

Note: We can check whether the given solution is correct or wrong. To check we need to substitute values of ‘m’ and ‘n’ in the given problem we have
\[\dfrac{1}{2}m - \dfrac{3}{4}n = 16\]
Put \[n = 8\] and \[m = 44\]
\[\dfrac{1}{2} \times 44 - \dfrac{3}{4} \times 8 = 16\]
\[22 - 6 = 16\]
\[ \Rightarrow 16 = 16\]
Hence the given answer is correct.
 If we want to transpose the addition number to any side of the equation we subtract it with the same number on both sides of the equation. Similarly if we want to transpose the negative number to any side of the equation we add with the same number on both sides of the equation. 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.