Question

Solve the following equation, check your result: $\dfrac{x}{2} + \dfrac{x}{4} = \dfrac{1}{8}$

Answer 1

Hint: To solve this type of linear equation we will take variable terms to one side and constants to the other side then we will apply different mathematical operations to get the required solution.

Complete step by step answer:
Since given that the equation $\dfrac{x}{2} + \dfrac{x}{4} = \dfrac{1}{8}$ and then we need to find the value of the unknown variable $x$, so we will make use of the basic mathematical operations to simplify further.
Starting with the cross-multiplication method we have, $\dfrac{x}{2} + \dfrac{x}{4} = \dfrac{1}{8} \Rightarrow \dfrac{{4x + 2x}}{{2 \times 4}} = \dfrac{1}{8}$
Now by the addition and multiplication operation, we get $\dfrac{{6x}}{8} = \dfrac{1}{8}$ (like $4x + 2x = x(4 + 2) = 6x$ also applicable for the variables)
Now cancel out the common terms by the division operation, then we have $\dfrac{{6x}}{8} = \dfrac{1}{8} \Rightarrow 6x = \dfrac{1}{8} \times 8 \Rightarrow 1$
Thus, again by the division operation, we get, $6x = 1 \Rightarrow x = \dfrac{1}{6}$ or $x = 0.166$ in decimal.
Hence the unknown value of the given variable is $x = \dfrac{1}{6}$ or $x = 0.166$

Note:
There are three methods to solve linear equations in one variable.
1. Trial and Error.
2. Inverse operations.
3. Transposition Method.