Question

How do you solve \[\dfrac{x}{5} - \dfrac{x}{2} = 3 + \dfrac{{3x}}{{10}}\]?

Answer 1

Hint: In the given problem we need to solve this for ‘x’. We solve this by taking LCM and then 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, with the aim of bringing like terms together and isolating the variable (or the unknown quantity). That is we group the ‘x’ terms one side and constants on the other side of the equation.

Complete step-by-step solution:
Given, \[\dfrac{x}{5} - \dfrac{x}{2} = 3 + \dfrac{{3x}}{{10}}\].
We know that the LCM of 5 and 2 is 10 and LCM on the right hand side of the equation is 10,
\[\dfrac{{2x - 5x}}{{10}} = \dfrac{{30 + 3x}}{{10}}\]
Multiplying 10 on both sides of the equation we have,
\[2x - 5x = 30 + 3x\]
We transpose ‘3x’ which is present in the right hand side of the equation to the left hand side of the equation by subtracting ‘3x’ on the left hand side of the equation.
\[2x - 5x - 3x = 30\]
Adding like terms we have,
\[ - 6x = 30\]
Divide the by -6 on both sides of the equations,
\[x = \dfrac{{30}}{{ - 6}}\]
\[ \Rightarrow x = - 5\].

Thus the required x value is x=-5.


Note: We can check whether the obtained solution is correct or wrong. All we need to do is substituting the value of ‘x’ in the given problem.
\[ \Rightarrow \dfrac{x}{5} - \dfrac{x}{2} = 3 + \dfrac{{3x}}{{10}}\]
\[ \Rightarrow \dfrac{{ - 5}}{5} - \dfrac{{ - 5}}{2} = 3 + \dfrac{{3( - 5)}}{{10}}\]
\[ \Rightarrow - 1 + \dfrac{5}{2} = 3 - \dfrac{3}{2}\]
Taking LCM and simplifying we have
\[ \Rightarrow \dfrac{{ - 2 + 5}}{2} = \dfrac{{6 - 3}}{2}\]
\[ \Rightarrow \dfrac{3}{2} = \dfrac{3}{2}\].
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.