Solve the linear equation $4x-10=-22$.

Hint: Solving an equation depends on the number of variables present in the equation as well as the type of the equation. For a set of linear equations, we will follow one method and for a quadratic equation we will follow another method likewise for a different type of equation we will follow different methods to solve the given equation. In the problem we have an equation which is a linear equation in one variable. To solve this type of equation we need to apply reverse arithmetic operations to the quantities involved in the given equation. While applying the athematic operations we need to follow some order which is the same as the order of operation. After doing all those operations we will get the result.

Complete step-by-step solution:
Given that,
$4x-10=-22$.
In the above equation we have the quantity $10$ which is involved in subtraction. We know that addition is the reverse arithmetic operation for the subtraction, so we will add $10$ on both sides of the above equation, then we will get
$4x-10+10=-22+10$
We know that $-a+a=0$, then
$4x=-12$.
In the above equation we have the quantity $4$ which is involved in multiplication. We know that division is the reverse arithmetic operation for multiplication, so we will divide the above equation with $4$ on both sides, then we will get
$\begin{align}
  & \dfrac{4x}{4}=\dfrac{-12}{4} \\
 & \Rightarrow x=-3 \\
\end{align}$
$\therefore $ The solution for the equation $4x-10=-22$ is $x=-3$.

Note: We can also solve this problem by using trial and error method which is nothing but substituting the $x$ values from $0$ to $\pm a$ where $\pm a$ is the value which satisfies the given equation.
Substituting $x=0$ in the given equation, then
$\begin{align}
  & 4\left( 0 \right)-10=-22 \\
 & -10\ne -22 \\
\end{align}$
So $x=0$ is not a solution.
Substituting $x=1$ in the given equation, then
$\begin{align}
  & 4\left( 1 \right)-10=-22 \\
 & -6\ne -22 \\
\end{align}$
So $x=1$ is not a solution.
Substituting $x=-1$ in the given equation, then
$\begin{align}
  & 4\left( -1 \right)-10=-22 \\
 & -14\ne -22 \\
\end{align}$
So $x=-1$ is not a solution.
Similarly
Substituting $x=-3$ in the given equation, then
$\begin{align}
  & 4\left( -3 \right)-10=-22 \\
 & -22=-22 \\
\end{align}$
So $x=-3$ is the solution.