Question

If $3\dfrac{1}{x} \times 3\dfrac{3}{4} = 12\dfrac{1}{2}$ , then the value of $x$ is
A. $1$
B. $\dfrac{1}{3}$
C. $2$
D. $3$

Answer 1

Hint: We have to find the value of $x$ the above question. We will first try to simplify the given mixed fractions into simpler forms and then we solve it. We should also note that the above equation can also be classified as the linear equation in one variable.
As we know that a linear equation is an algebraic equation which is of the form
$y = mx + b$ . It involves only a constant and a first-order term also called a linear form, where $m$is the slope and $b$is the $y$- intercept.
We should know that the general form of linear equation in one variable is written as $ax + b = 0$ i.e. only one variable.

Complete step by step solution:
Here we have $3\dfrac{1}{x} \times 3\dfrac{3}{4} = 12\dfrac{1}{2}$.
Let us write the above equations in a simpler form by breaking the mixed fractions i.e.
$ \Rightarrow \dfrac{{3x + 1}}{x} \times \dfrac{{15}}{4} = \dfrac{{25}}{2}$
We will now multiply the values above:
$ \Rightarrow \dfrac{{15(3x + 1)}}{{4x}} = \dfrac{{25}}{2}$
$ \Rightarrow \dfrac{{45x + 15}}{{4x}} = \dfrac{{25}}{2}$
Now we will cross multiply the values:
$2(45x + 15) = 25 \times 4x$
Upon cross multiplication, we have:
$ \Rightarrow 90x + 30 = 100x$
We will arrange the similar terms together;
$ \Rightarrow 100x - 90x = 30$
It gives us:
$ \Rightarrow 10x = 30$
Therefore we have value
$x = \dfrac{{30}}{{10}} = 3$

So, the correct answer is “Option (d)”.

Note: We should note that we can always verify our solution by substituting the value into the left side of the equation and if it equals the right side then it is the correct solution. From the above question, it can be noted that this is a question of linear equation in one variable as we can solve it can by using the basic knowledge of arithmetic operators but while calculating we should be careful as in such types of the questions because calculation mistake is possible also with the positive and negative signs of the numbers and variables. We should also know that if we make the graph of a linear equation, it will have a straight line, this will happen when the highest power of the given variable is $1$ . It is classified into different types based on the number of variables like a linear equation in one variable or a linear equation in two variables.