Also in 2026 Practice Test A Math, question 6; 2025 Practice Test A Math, question 7.
Question
- A
- B
- C
- D
Show the answer
Correct answer: A
Question analysis
An expression question: simplify a sum and difference of two linear expressions in n. Students remove the parentheses, subtract every term inside the second group, and combine like terms. The minus sign in front of the second parentheses is the trap, since it has to change the sign of both terms inside.
- NYS standards
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- At grade 7 Simplifying linear expressions with a subtracted group is standard grade 7 work. This is a typical textbook exercise in length, with the usual sign trap and no extra steps or real-world context.
- Estimated difficulty
- Straightforward: two steps or one careful reading.
- Thinking it demands
- Depth of knowledge 1, recall and reproduction · mainly apply
- What makes it hard
- Error-prone arithmetic moderate
- A very close wrong answer moderate
- Solution
- 2 steps
- Reading level
- Question and choices: about grade 16+, 5 words.
- Corrected from the DOE handbook
- The handbook’s answer key for this question was corrected.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
There are only five terms, but two signs decide the answer: the minus in front of the second parentheses and the sign left after 3n − 4n. Each wrong choice comes from one or both of those sign decisions, so all of them look plausible, and checking needs care rather than time. Even the DOE handbook keyed the version with the wrong sign on n.
Error-prone arithmetic moderate Working it out
The minus sign before (4n + 8) has to reach both terms, making −4n and −8, and 3n − 4n leaves a negative n term. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
A very close wrong answer moderate Choosing the answer
5 − n and 5 + n are written alike and share the constant 5; only the sign of the n term, from 3n − 4n, separates them, and the DOE handbook's own key picked the wrong one. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Strategy: Rewrite the subtraction as adding the opposite of each term in the second parentheses, then group the constants and the n terms separately.
Traps
- Order of operations: Working left to right, or distributing a minus sign wrongly, gives a choice.
- Negatives and direction: Arithmetic with negative numbers, the order of a subtraction, or direction on a number line. (Moving a term across the equals sign without changing its sign is a faulty procedure.)
The wrong answers, classified
B Negatives and direction (Brown & Burton, 1978)
Gets the constants right, 7 + 6 − 8 = 5, but writes 3n − 4n as +n, subtracting the smaller coefficient from the larger and keeping a plus sign.
C Order of operations (Brown & Burton, 1978)
Applies the minus sign to 4n but not to 8, so the constants become 7 + 6 + 8 = 21 while the n term comes out right.
D Order of operations (Brown & Burton, 1978)
Makes both mistakes: adds the 8 instead of subtracting it, for 21, and also writes 3n − 4n as +n.
What was corrected from the DOE handbook, and why
- Answer key: The handbook (its question 64) keys this question as F, which is 5 + n (choice B here), in its answer key and in the heading of its explanation. Its own working gives 7 + 3n + 6 − 4n − 8 = 5 − n, which is the handbook’s choice E and choice A here, and that is correct. The key here is A.
Worked solution, step by step
Formulas used
- Subtracting a group in parentheses
- a and b are the terms inside the parentheses. A term is a number, a letter, or a number times a letter. The minus sign in front means you subtract the whole group. So you subtract every term inside, not just the first one.
- Combining like terms
- n stands for an unknown number, and 3n means 3 times n. Like terms have the same letter part, like 3n and 4n. To combine them, add or subtract the numbers in front and keep the letter. Plain numbers combine only with plain numbers.
Sort out the question
You need to simplify the expression, which means write it in a shorter form. An expression is a math phrase made of numbers, letters and signs. Here n stands for an unknown number. Find the choice that matches the short form.
Remove the parentheses
The first group has a plus sign in front. Adding a group changes nothing, so is just . The second group has a minus sign in front. You must subtract both terms inside it.
Watch out: the minus reaches the 8 too. Adding the 8 instead gives 21 for the plain numbers. That leads to choice C or D.
Combine the plain numbers
Group the numbers without a letter. Work them out from left to right.
The plain numbers make 5.
Combine the n terms
You have 3 n’s, and you take away 4 n’s. The numbers in front give 3 − 4 = −1. So you are left with −1n, which is written −n.
Watch out: it is easy to write +n here. That gives 5 + n, choice B.
Put the two parts together
Join the number part and the n part. Adding a negative is the same as subtracting.
So the answer is A, 5 − n.
Check your answer
Pick any number for n and test it. Try n = 1. The original: . Choice A: . They match. Choice B gives , which does not.
More questions like this
The original DOE question
