Question

Give the first step you will use to separate the variable and then solve the equation: $3l=42$.

Answer 1

Hint: To solve the question we need to know the concept of cross multiplication. In cross multiplication the numerator in the LHS when taken to RHS becomes the denominator in RHS. The value of $l$ will be found using the cross multiplication.

Complete step by step answer:
The question asks us to find the value of the unknown variable given to us. In the question we are given that when $3$ is multiplied to an unknown variable $l$, its results into another number called $42$. Mathematically it is written as:
$\Rightarrow 3l=42$
To solve the problem the first step will be to cross multiply the number so that the unknown variable $l$ could be found. For doing this the coefficient of $l$ which is $3$ will be taken to the RHS side where it will divide the number present in the Right Hand Side, in our problem it is $42$. On writing the above explanation in mathematical form we get:
$\Rightarrow l=\dfrac{42}{3}$
In the above fraction we see that the numerator and the denominator have a common factor which is $3$. So on dividing each of the numerator and the denominator by $3$ we get:
$\Rightarrow l=\dfrac{\dfrac{42}{3}}{\dfrac{3}{3}}$
On solving the above expression we get:
$\Rightarrow l=\dfrac{14}{1}$
Fraction with the denominator as $1$ is the same as the natural number present in the numerator.
$\Rightarrow l=14$
$\therefore $ The value of the variable given in the question $3l=42$ is, $14$.

Note: Cross Multiplication is an important operation used to find the unknown variable for certain mathematical problems. In case of cross multiplication the operation done by a number in LHS changes on RHS.