Question

How do you solve $\dfrac{x}{3}+\dfrac{x}{2}=15$?
 (a) Using algebraic properties
(b) Using trigonometric identities
(c) a and b both
(d) None of these

Answer 1

Hint: To start with, we have, $\dfrac{x}{3}+\dfrac{x}{2}=15$. We get on with adding the two terms given on the left hand side. Thus we get a value of $\dfrac{5x}{6}$which is equal to 15. Hence, from there we are finding the value of x cross multiplying the values and fixing x.

Complete step by step answer:
According to the question, we have, $\dfrac{x}{3}+\dfrac{x}{2}=15$,
From the left hand side,
$\Rightarrow \dfrac{x}{3}+\dfrac{x}{2}$
Here, first we are trying to find the L.C.M of the numbers 3 and 2.
As, both of them are prime numbers, the lcm would be the multiplication of the numbers,
So, the lcm is, $\left( 3\times 2 \right)=6$
Then, to find the sum,
 $\Rightarrow \dfrac{2x+3x}{6}$
Adding 2x and 3x we get, 5x,
$\Rightarrow \dfrac{5x}{6}$
And we also have, the right hand side is equal to, 15,
Thus, we get, equaling them, $\dfrac{5x}{6}=15$
Dividing both sides by 5, we are getting,
$\Rightarrow \dfrac{x}{6}=3$
Multiplying both sides by 3 we get, x = 18,
So, we have just used the algebraic properties to find the solution.

So, the correct answer is “Option a”.

Note: While solving this question, the possible mistake one can make is all at the time of doing basic algebraic calculations or while taking the least common multiple of the question. Also, we can solve this question by first taking x common and then taking LCM and then simplifying which will also give us the correct answer.