Question

Find the value of x in the equation, $\dfrac{{12}}{x} = \dfrac{3}{4}$

Answer 1

Hint: Cross multiplication is the key here. Once you have cross multiply the fractions on both sides, you’ll see a linear equation in place. Last step will be the use of a basic operation that is to be applied on both the sides to get the final answer. In case of more complex equations, one might have to use a combination of different operations, i.e., multiplication, division, addition and subtraction.

Complete answer:
Let us denote the sides as Left-hand side (LHS) and Right-hand side (RHS).
$\dfrac{{12}}{x} = \dfrac{3}{4}$
Now, we need to cross multiply the denominator of LHS to the numerator of the RHS and the denominator of the RHS to the numerator of the LHS. The resulting equation will be,
$ \Rightarrow 12 \times 4 = 3 \times x $
$ \Rightarrow 48 = 3x $
Now, to isolate x on the RHS divide both the LHS and the RHS by 3.
${
   \Rightarrow \dfrac{{48}}{3} = \dfrac{{3x}}{3} \\
   \Rightarrow 16 = x \\
} $
Thus, the value of $x = 16$.
Additional Information: One can also solve this by taking the whole fraction on the left-hand side to the right hand side.
\[
  \dfrac{{12}}{x} = \dfrac{3}{4} \\
   \Rightarrow \dfrac{3}{4} = \dfrac{{12}}{x} \\
   \Rightarrow \dfrac{3}{4} - \dfrac{{12}}{x} = 0 \\
    \\
\]
Now, taking the LCM of the denominators of the fractions and making changes in the numerators accordingly, the equation changes to
$ \Rightarrow \dfrac{{3x - 48}}{{4x}} = 0$
Multiplying 4x on both the sides, we have
$ \Rightarrow 3x - 48 = 0$
Adding 48 on both the sides,
$3x = 48$
Dividing both the sides with 3,
$x = 16$

Note: A linear equation is an equation that can be put in the form of the variables and the coefficients, mostly real numbers. Coefficients may be equation parameters or arbitrary expressions, provided that they do not include any of the variables. First order equations are linear equations.