How do you solve $3x-1=8$?

Hint: We have a linear equation in one variable. We will rearrange the terms in the given equation such that the constant terms are on one side of the equation and the variable term on the other side of the equation. We will simplify the obtained equation by doing the arithmetic operations in the equations. After that we will solve for $x$ to obtain the required solution.

Complete step-by-step solution:
The given equation is $3x-1=8$. We will rearrange the terms in this equation so that we have the constant terms on one side of the equation and the variable term on the other side of the equation. We will shift the $-1$ to the right hand side of the given equation. So, we get the following equation,
$3x=8+1$
Now, we will simplify this obtained equation by doing the arithmetic operation present on the right hand side of the equation. So, we get the following,
$3x=9$
Dividing both sides of the equation by 3, we get
$\begin{align}
  & \dfrac{3x}{3}=\dfrac{9}{3} \\
 & \therefore x=3 \\
\end{align}$
Hence, $x=3$ is the solution of the given equation.

Note: The highest degree of the given equation is 1. Hence, it is a linear equation. The linear equation in one variable has one solution. If the highest degree of an equation is 2, it is called a quadratic equation. We get two solutions for a quadratic equation. If the highest degree of an equation is 3, then it is called the cubic equation. We should be careful with the signs of the terms while shifting them from one side of the equation to the other.