Question

Find the solution of \[\dfrac{x}{6} + 4 = 15\].

Answer 1

Hint: Such questions can be done by taking the LCM that is the lowest common multiple of both the fractions. Here the lowest common multiple can be taken of 6 and 1. Also, 4 can be taken right hand side and by cross multiplication and further evaluation can be done. Such fractions do not require a lengthy process and can be solved easily by mentioning two methods.

Complete answer:
According to the question we have,
\[\dfrac{x}{6} + 4 = 15\]
Taking the LCM that is lowest common multiple of both 6 and 1 we have,
\[ \Rightarrow \dfrac{{x + 24}}{6} = 15\]
Since the LCM is 6 and 6 when divided by 6 gives 1 and when 1 is multiplied by x it gives x. In the same way 1 when divided by 6 gives 6 and then 6 is multiplied by 4 which gives 24.
Now, cross multiplying the above we have,
\[
   \Rightarrow x + 24 = 90 \\
   \Rightarrow x = 90 - 24 \\
   \Rightarrow x = 66 \\
 \]
Hence, the value of x for \[\dfrac{x}{6} + 4 = 15\] is 66.

Note: From the question\[\dfrac{x}{6} + 4 = 15\], 4 can be taken to the right hand side and can be subtracted by 15 which gives 11. Then x can be easily obtained by cross multiplying 11 and 6. Hence in this way also the result will be 66. Hence, this can be solved by two simpler methods. It is important to take care of the signs whenever there is a shift from LHS to RHS or vice versa otherwise in the answer the sign may change. Also when there is a shift from one side to other multiplication will be divided the other side and vice versa.