Question 130·Easy·Equivalent Expressions
Which expression is equivalent to ?
For expression-equivalence questions involving subtraction of parentheses, first rewrite the expression without parentheses by distributing the minus sign to every term in the second group, then combine like terms (variables with variables, constants with constants). Work systematically to avoid sign errors: explicitly write the intermediate step with all signs changed before simplifying, and then match your simplified expression to the answer choices.
Hints
Think about the subtraction sign
You are subtracting the entire expression . How does that subtraction affect both and inside the parentheses?
Remove the parentheses carefully
Rewrite without parentheses by distributing the minus sign to each term in before you combine anything.
Combine like terms
After you remove parentheses, group the -terms together and the constant numbers together. What do and simplify to?
Desmos Guide
Enter the original expression as a function
In Desmos, replace with for graphing. Type f(x) = (5x - 3) - (2x + 7) to represent the original expression.
Enter each answer choice as a separate function
Type each choice (again using instead of ) as g(x) = 3x + 4, h(x) = 3x - 10, p(x) = 7x + 4, and q(x) = 7x - 10.
Compare the graphs
Look at the graphs of all these functions. The correct choice is the one whose line lies exactly on top of the graph of for every -value, meaning the two expressions are equivalent.
Step-by-step Explanation
Rewrite the subtraction without parentheses
Start with the expression
Subtracting a group means you are adding its opposite. Distribute the minus sign to both terms in :
Group like terms
Now group the -terms together and the constant terms together:
- are the like terms with .
- are the constant terms.
So you have:
Combine like terms and match to a choice
Combine the like terms:
- For the -terms: .
- For the constants: .
So the simplified expression is
which matches answer choice B.