Which of the following expressions is equivalent to ?
For expression-equivalence questions like this, immediately apply the distributive property to remove parentheses, paying close attention to negative signs. Then combine like terms—first group all terms, then all constant terms—to get a simplified expression. Avoid mental shortcuts with signs; writing out each distribution step clearly is fast and prevents common mistakes on test day.
Hints
Use the distributive property
Focus on removing the parentheses by multiplying the number outside each parenthesis by each term inside. What do you get for and for ?
Be careful with the negative sign
The expression has , not . How does the negative sign affect both and when you distribute?
Combine like terms
Once you distribute, you will have some terms and some constant numbers. Group the terms together and the constants together, then add them.
Desmos Guide
Enter the original expression
In Desmos, type y = 3(x + 4) - 2(x - 1) to graph the original expression.
Enter each answer choice as a separate function
Type each choice as its own function, for example y = x + 10, y = 5x + 10, y = x + 7, and y = x + 14, so you have the original graph and four option graphs on the same coordinate plane.
Compare the graphs
Look for the option whose graph lies exactly on top of the graph of y = 3(x + 4) - 2(x - 1) for all values of . That option is the equivalent expression.
Step-by-step Explanation
Distribute in the first term
Start with the expression:
Distribute the 3 across the parentheses:
So the expression becomes:
Distribute in the second term
Now distribute the across .
Remember that the applies to both and :
Substitute this into the expression:
Combine like terms
Group and combine the terms and the constant terms separately:
- Combine the terms: .
- Combine the constants: .
So the simplified expression is:
Therefore, the equivalent expression is .