Which expression is equivalent to ?
For equivalent expression questions, first apply the distributive property correctly, being very careful with negative signs, then combine like terms (all the x-terms together, all constants together). Do the algebra step by step on paper to avoid mental errors, and if you are unsure between two options, plug in a simple value for x (like 0 or 1) into both the original expression and the choices to see which one always matches.
Hints
Look at the parentheses first
Focus on the part before worrying about the . What property lets you multiply 4 by both terms inside the parentheses?
Distribute carefully with signs
When you multiply 4 by and by , pay attention to the negative sign on the 2. What are the two terms you get after distributing?
Combine like terms
After distributing, you will have two terms and one constant. Which terms have , and how do you combine them? What happens to the constant term?
Desmos Guide
Enter the original expression
In Desmos, type y = 4(3x - 2) - 5x to represent the original expression as a function.
Enter each answer choice as a separate function
On new lines, enter y = 17x - 8, y = 7x + 8, y = 12x - 13, and y = 7x - 8. You will now have the original expression and all four choices graphed together.
Compare graphs or use a table
Either:
- Look at the graphs and see which line lies exactly on top of the graph of
y = 4(3x - 2) - 5xfor all x, or - Turn on a table for each function and compare a few x-values (for example x = 0, 1, 2). The correct choice will match the original expression’s y-values for every tested x.
Step-by-step Explanation
Distribute the 4
Start with the expression .
Distribute the 4 to both terms inside the parentheses:
So becomes .
Now the whole expression is .
Combine like terms
Combine the terms and .
Keep the constant term unchanged; only combine like terms.
Match with the answer choices
The simplified form of is .
Looking at the choices, this matches choice D.