Question

Solve: $\dfrac{x}{2} + \dfrac{x}{4} = \dfrac{1}{8}$

Answer 1

Hint:$x$ is a variable term whose value is to be found by the following calculations. Take LCM which is abbreviated as Least Common Multiple of the denominator on the left hand side to make the denominators of both the terms equal to each other. Now, as we will have the same denominators, we will cross multiply the denominators or directly equate numerators on both sides.

Complete step by step answer:
$\dfrac{x}{2} + \dfrac{x}{4} = \dfrac{1}{8}$
Take LCM i.e. Least Common Multiple of the denominator on left hand side, we get
$\dfrac{{2x + x}}{4} = \dfrac{1}{8}$
Adding the quantities in numerator, we get
$\dfrac{{3x}}{4} = \dfrac{1}{8}$
On cross multiplication, we get
$8(3x) = 4(1)$
On solving further we get
$24x = 4$
Taking all the numerical terms on one side and the variable terms on the other side we get the following result :
$x = \dfrac{4}{{24}}$
On simplifying, we get
$\therefore x = \dfrac{1}{6}$

Therefore the final value of $x = \dfrac{1}{6}$.

Note: If you do not find it comfortable to take the LCM i.e. Least Common Multiple of denominators on left hand side to make the denominators of both the terms equal to each other then you can also follow the solution below:
$\dfrac{x}{2} + \dfrac{x}{4} = \dfrac{1}{8}$
Multiply both the sides with $8$ we get
$8\left( {\dfrac{x}{2} + \dfrac{x}{4}} \right) = 8\left( {\dfrac{1}{8}} \right)$
Separating the terms in left hand side we get
$8\left( {\dfrac{x}{2}} \right) + 8\left( {\dfrac{x}{4}} \right) = 1$
On simplifying the above equation we get
$4x + 2x = 1$
On addition of terms in the left hand side we get
$6x = 1$
Taking all the numerical terms on one side and the variable terms on the other side we get the following result :
$x = \dfrac{1}{6}$
Therefore the final value of $x = \dfrac{1}{6}$. We can check whether the obtained solution is correct or not by substituting the value in the given equation.