Determine whether the given problem is an equation or an expression. If it is an...

Step 1
We have to determine whether the given problem is equation or expression. If it is an equation then we have to solve and if it is expression then simplify where problem is:
${\displaystyle \frac{5n}{6}-\frac{n}{8}=-\frac{17}{12}}$
We know that
Expression can be any numbers, variables or combination of number and variable connected through mathematical operations.
Example:
${\displaystyle 3,x^2,5+17x}$, ...
Equation is connected through equal sign where each side should be any expression.
Example:
${\displaystyle x=y,x^2+3=0,x^2+2x=7}$, ...
The given problem have two expressions connected through equal sign.
Hence, it is an equation.
Step 2
Now solving the equation by taking LCM of the denominator in LHS side, we get
${\displaystyle \frac{5n}{6}-\frac{n}{8}=-\frac{17}{12}}$
${\displaystyle \frac{5n\times 4-3\times n}{24}=-\frac{17}{12}}$
${\displaystyle \frac{20n-3n}{24}=-\frac{-17}{12}}$
${\displaystyle \frac{17n}{24}=-\frac{17}{12}}$
${\displaystyle 12\times 17n=-17\times 24}$
${\displaystyle n=\frac{-17\times 24}{12\times 17}}$
=-2
Hence, solution of the equation is n=−2.