After you expand, pay close attention to the minus sign in front of the second parentheses. How does subtracting $(2/3x - 8/3)$ affect the signs of $2/3x$ and $-8/3$?

You will have two $x$-terms and two constant terms, all involving fractions. Use a common denominator to combine the $x$-terms, and then add the constants.

In Desmos, on one line type the original expression:

(5/6)*(3x+2) - (2/3)*(x-4)

This will graph the line that represents the given expression.

On four new lines, type each choice as a separate expression, for example:

(11/6)x - 13/3, (1/6)x + 13/3, (11/6)x + 5/3, and (11/6)x + 13/3.

Each one will appear as its own line on the graph.

Compare the graphs: the choice whose line lies exactly on top of the graph of the original expression for all values of $x$ is the equivalent expression.

Distribute each fraction across its parentheses using the rule $a(b+c)=ab+ac$.

• First group: $(5/6)(3x+2) = (5/6)(3x) + (5/6)(2) = 5/2x + 5/3$.
• Second group: $(2/3)(x-4) = (2/3)(x) + (2/3)(-4) = 2/3x - 8/3$.

So the expression becomes $5/2x + 5/3 - (2/3x - 8/3)$.

Remove the parentheses around the second group. Because there is a minus sign in front, you must change the sign of each term inside.

We have $-(2/3x - 8/3) = -2/3x + 8/3$.

So the whole expression is $5/2x + 5/3 - 2/3x + 8/3$.

Combine like terms.

First combine the $x$-terms:

$5/2x - 2/3x$.

Use a common denominator of 6: $5/2 = 15/6$ and $2/3 = 4/6$, so $5/2x - 2/3x = 15/6x - 4/6x = 11/6x$.

Then combine the constants: $5/3 + 8/3 = 13/3$.

So the simplified expression is $11/6x + 13/3$, which matches choice D.