Which expression is equivalent to ?
For expression-equivalence questions like this, first expand any parentheses using the distributive property, then carefully deal with minus signs in front of parentheses by changing the signs of all terms inside. Once all parentheses are removed, combine like terms (group -terms together and constants together) to simplify. Work step by step and pay special attention to signs, since most wrong answers come from sign errors rather than difficult algebra.
Hints
Start by expanding
First, ignore the answer choices and expand using the distributive property.
Handle the subtraction sign correctly
Look carefully at the minus sign before . How does subtracting a whole parentheses affect each term inside it?
Combine like terms at the end
After you remove the parentheses, group the -terms together and the constant numbers together, then simplify.
Desmos Guide
Enter the original expression as a function
In the first line, type y1 = 4(2x - 3) - (5x - 1) so Desmos graphs the original expression as a line.
Enter each answer choice as separate functions
On new lines, type each option as y2 = 3x - 11, y3 = 13x - 13, y4 = 3x + 11, and y5 = -3x - 11 (order doesn’t matter as long as you know which is which).
Compare the graphs to find the match
Look to see which of the lines from the answer choices lies exactly on top of the graph of for all -values. The choice whose line perfectly overlaps is the equivalent expression.
Step-by-step Explanation
Distribute the 4 across the first parentheses
Apply the distributive property to .
So the original expression becomes:
Remove the second parentheses carefully
A minus sign in front of parentheses means you subtract each term inside, which is the same as multiplying by .
Now there are no parentheses, and you can combine like terms.
Combine like terms to simplify
Group the -terms together and the constant terms together:
So the simplified, equivalent expression is , which matches choice D.