How do you solve $3x+15=8x-24$?

Hint: For this problem we need to solve the given equation and find the value of $x$. We can observe that a given equation is a linear equation in a single variable. So, we will perform the reverse arithmetic operation for the arithmetic operation which we have in the equation. So, we will first rearrange the terms in the given equation, so that all the variables are at place and all the constants are one place. Now we will simplify the equation by using the arithmetic operations. After that we will divide the whole equation with the coefficient of the $x$ and simplify the equation to get the value of $x$.

Complete step-by-step solution:
Given equation, $3x+15=8x-24$.
Rearranging the terms in the above equation, so that all the variables are at one place and all the constants are at one place. For this we are first shifting the variable $3x$ which is left hand side to the right-hand side and changing its sign, then we will get
$\Rightarrow 15=8x-24-3x$
Now shifting the constant $-24$ which is right hand side to the left-hand side and changing its sign, then we will have
$\Rightarrow 15+24=8x-3x$
Simplifying the above equation, then we will get
$\Rightarrow 5x=39$
In the above equation we have the coefficient of $x$ as $5$. Dividing the above equation with $5$ on both sides of the above equation, then we will get
$\begin{align}
  & \Rightarrow \dfrac{5x}{5}=\dfrac{39}{5} \\
 & \Rightarrow x=\dfrac{39}{5} \\
\end{align}$
Hence the solution of the given equation $3x+15=8x-24$ is $x=\dfrac{39}{5}$.

Note: We can also check whether the obtained solution is correct or wrong by substituting the calculated value in the given equation and simplifying it. In some cases, they may ask to justify your solution, then we need to check whether the solution is correct or wrong by substituting the calculated value in the above equation. Otherwise, it is not necessary.