Question

Solve $\dfrac{3}{4} = \dfrac{3}{8}x - \dfrac{3}{2}$?

Answer 1

This problem deals with solving the linear equation with one variable. A linear equation is an equation of a straight line, written in one variable. The only power of the variable is 1. Linear equations in one variable may take the form of $ax + b = 0$, and are usually solved for the variable $x$ using basic algebraic operations.

Complete step by step solution:
Given a linear equation one variable, here the variable is $x$, which is considered as given below:
$\Rightarrow \dfrac{3}{4} = \dfrac{3}{8}x - \dfrac{3}{2}$
Now rearrange the terms such that all the constants are on one side of an equation and all the $x$ terms are on the other side of the equation.
Now moving the constant $\dfrac{3}{2}$ which is on the right hand side of the equation to the left hand side of the equation, as shown below:
$\Rightarrow \dfrac{3}{4} + \dfrac{3}{2} = \dfrac{3}{8}x$
Now simplifying the above equation, as the like terms are and the constants are grouped together, the constants $\dfrac{3}{4}$ and $\dfrac{3}{2}$ are simplified on the left hand side of the equation, as shown below:
$\Rightarrow \dfrac{3}{8}x = 3\left( {\dfrac{3}{4}} \right)$
Now cancel 3 in the numerators and 4 in the denominators of both sides of the equation, as shown below:
$\Rightarrow \dfrac{1}{2}x = 3$
Now multiply the above equation with 2, to get the value of $x$, as shown below:
$\Rightarrow x = 6$

Note: Please note that the linear equations in one variable which are expressed in the form of $ax + b = 0$, have only one solution. Where $a$ and $b$ are two integers, and $x$ is a variable. This means that there will be no terms involving higher powers of $x$ not even the power of 2, which is ${x^2}$.