In the equation $5(k-2)+m=n$, what can you replace $n$ with in the expression $n-m$?

After substitution, you will have something like "$\dots + m - m$". What happens to the $m$ terms? Then, look at $5(k-2)$: how do you expand this using the distributive property?

In a Desmos expression line, type 5(k-2)+m - m. This corresponds to substituting $n = 5(k-2)+m$ into $n-m$ and then subtracting $m$.

Desmos will automatically simplify the expression you typed. Look at the simplified algebraic form it displays; that is the expression for $n-m$ in terms of $k$ (you should see a linear expression in $k$ only).

You are given the relationship

and you are asked to rewrite $n-m$ using only the variable $k$ (no $m$ or $n$ left in the final expression).

From the equation, $n$ equals $5(k-2)+m$.

So replace $n$ in $n-m$ with this expression:

Now simplify the expression $[5(k-2)+m] - m$.

Inside the brackets you have $+m$, and outside you subtract $m$:

Since $m - m = 0$, the $m$ terms cancel out, leaving

as the expression for $n-m$ in terms of $k$. This is almost in the same format as the answer choices, but not yet fully expanded.

Distribute the $5$ in $5(k-2)$:

So

This matches answer choice D) $5k-10$.