How do you solve $\dfrac{5}{4}x+\dfrac{1}{8}x=\dfrac{9}{8}+x$ ?

Hint: The equation given in the question is a linear equation in one variable , so just one equation is enough to solve for the unknown variable. We can solve it by bringing all x to one side and all the constant to another side and then divide both LHS and RHS by coefficient of x.

Complete step by step answer:
The given equation is $\dfrac{5}{4}x+\dfrac{1}{8}x=\dfrac{9}{8}+x$ , which is a linear equation
Let’s bring all x to RHS and constant to LHS to solve it.
We can see there is a term x in RHS so we can send it to LHS by subtracting x form LHS and RHS
$\Rightarrow \dfrac{5}{4}x+\dfrac{1}{8}x-x=\dfrac{9}{8}$
Now we can see all the x terms in the LHS and constant in RHS. Adding all the fractions in LHS we get
 $\Rightarrow \dfrac{3}{8}x=\dfrac{9}{8}$
Now we can get the value of x by dividing both LHS and RHS by $\dfrac{3}{8}$
$\Rightarrow x=3$
So the value of x that satisfy the equation $\dfrac{5}{4}x+\dfrac{1}{8}x=\dfrac{9}{8}+x$ is equal to 3.

Note:
We know that we only need one equation to solve a linear equation one variable, but we have a system of n different unknown variables, then we need at least n equations to solve for the unknowns. If we have n variables and less than n equations then the system will have an infinite number of solutions. If we have more than n equations there may not exist any solution for the system.