After you distribute the 2, focus on $5 - (a - 6)$. What happens to each term inside the parentheses when you subtract the whole group?

Once you rewrite $5 - (a - 6)$ as a simpler expression, you will still have a minus sign in front of that entire expression. How does that minus sign affect both terms inside the parentheses?

After all parentheses are removed, you should have a sum of $a$-terms and constants. Group the $a$-terms together and the constants together, then simplify.

In Desmos, type the original expression as a function of $a$, for example f(a) = 2(3a - 4) - (5 - (a - 6)).

Type each choice as its own function, for example g(a) = 7a - 19, h(a) = 5a + 2, j(a) = 7a + 19, and k(a) = 6a - 19.

Turn on the graphs for all functions. If one of the lines lies exactly on top of the graph of $f(a)$ for all values of $a$, that choice is equivalent to the original expression. You can also create a table for $f(a)$ and each choice at several $a$-values and look for the one whose values always match $f(a)$.

Start with the original expression:

Distribute the 2 to both terms inside the first parentheses:

So the expression becomes:

Focus on the part $5 - (a - 6)$. Subtracting a group means changing the signs of everything inside that group:

Now combine the constant terms $5$ and $6$:

So we can rewrite the whole expression as:

Now handle the minus sign in front of $(11 - a)$. Subtracting $(11 - a)$ is the same as adding $-11$ and $+a$:

Substitute this into the expression:

Now combine like terms in

• Combine the $a$ terms: $6a + a = 7a$.
• Combine the constants: $-8 - 11 = -19$.

So the simplified expression is

This matches choice A, so the correct answer is $7a - 19$.