Question 143·Medium·Equivalent Expressions
Which expression is equivalent to ?
For expression-equivalence questions, work systematically: first distribute multiplication over parentheses, then simplify any grouped expressions, paying extra attention to minus signs in front of parentheses. After everything is expanded, remove brackets by distributing any negatives, then combine like terms (all -terms together, all constants together). Finally, compare your simplified expression directly to the answer choices instead of trying to work backwards from them.
Hints
Start by expanding
Ignore the brackets for a moment and expand and using distribution.
Be careful with the minus sign
When you see , remember that the negative sign applies to both and . How does that change the signs of each term?
Subtracting a group
After you simplify inside the brackets to something like , think of as multiplying the inside by before combining like terms.
Combine like terms at the end
Once everything is expanded and the brackets are gone, group -terms together and constant terms together, then simplify.
Desmos Guide
Use Desmos to simplify the expression
In a new expression line, type 3(2x - 1) - (4(x - 3) - (x + 2)). Desmos will automatically simplify this expression; read the simplified form it shows (it should appear as 3x + 11), and then match that expression to the correct answer choice.
Step-by-step Explanation
Distribute in the first parentheses
Start with the part . Distribute the 3 to both terms inside the parentheses:
So the whole expression becomes:
Simplify the expression inside the brackets
Now focus on the bracketed part .
First distribute the 4:
Now subtract , remembering the minus applies to both and :
So the original expression is now:
Remove the brackets carefully
You are subtracting the entire quantity . Subtracting a group is the same as distributing to each term inside:
Now you have an expression without brackets: .
Combine like terms and match the answer choice
Combine the -terms and the constant terms:
So the simplified expression is .
Among the answer choices, this matches choice D, .