Question

Find the solution of \[x - \dfrac{1}{8} = \dfrac{3}{4}\].

Answer 1

Hint: Linear equations are the equations in which the variables are raised to the power equal to one. The linear equations are classified into different types based on the number of variables in the equation.

Complete step-by-step solution:
According to the question, to solve the given equation we should first evaluate it and give it a form of equation.
In order to isolate “x”, we should add \[18\] to both sides of the equation. This will keep the equation balanced and undo the \[ - 18\] already on the left hand side. This gives:
\[
  x - \dfrac{1}{8} + \dfrac{1}{8} = \dfrac{3}{4} + \dfrac{1}{8} \\
   \Rightarrow x = \dfrac{3}{4} + \dfrac{1}{8} \\
\]
In order to add fractions, we must have a common denominator. We can achieve this by multiplying \[\dfrac{3}{4}\] by \[\dfrac{2}{2}\], which is equal to\[1\]. This will change how the fraction looks but won't change its actual value.
\[
  x = \dfrac{3}{4}\left( {\dfrac{2}{2}} \right) + \dfrac{1}{8} \\
   \Rightarrow x = \dfrac{6}{8} + \dfrac{1}{8} \\
\]
Now that the fractions have equal denominators, we can add the numerators and keep the denominators the same.
\[
  x = \dfrac{{6 + 1}}{8} \\
   \Rightarrow x = \dfrac{7}{8} \\
\]
Hence, the solution is\[\dfrac{7}{8}\].

Note: Linear equations in one variable are the equation which consists of one variable. Linear equations in two variables are variables which have two variables. Standard method of linear equation eases the method of solving the equation. The linear equation in one variable is written in the form of\[ax + b = 0\]. The linear equation in two variables is written in the form of\[ax + by + c = 0\]. The linear equation in three variables is written in the form of\[ax + by + cz + d = 0\].