Week 2 — Solve It, Check It, Explain It: Equations and Inequalities

Assignment 2 of the term — solve four pinned equations and inequalities, check every answer by substitution, and explain one result to someone who has not taken algebra.

This adaptive assignment uses a coaching dialogue to help you turn a first attempt into a clear, checked set of solutions. You remain the author. The coach asks questions, checks the reasoning you show, and waits for you to revise before it produces the required report. Last week you learned to distribute, combine like terms, and follow the order of operations; this week those moves become the first steps of every solve. This week's lecture tutorial, quiz, discussion, and Model/Build Studio practice the same ideas from other angles; this assignment is where you put them together and defend each answer with a check.

The task

Work these four problems, showing every algebra step on its own line:

1. Solve 3(x − 2) = 2x + 5 for x.
2. Solve −2x + 1 < 9 and state the endpoint of the interval of x-values that work.
3. Solve |2x − 1| = 7 and give the larger of its two solutions.
4. Campus sits at mile marker 10 on a straight road, and you want an apartment within 2 miles of campus. Solve |m − 10| ≤ 2 and give the highest mile marker that qualifies.

Beside each answer, add one brief interpretation:

• For problem 1, show the check by substitution: evaluate both sides of the original equation at your answer.
• For problem 2, write the full solution set in interval notation, say whether the endpoint is included, and name the step where the inequality sign flips and why.
• For problem 3, give both solutions, check each one in the original equation, and say why an absolute-value equation can have two solutions.
• For problem 4, write the full set of qualifying mile markers in interval notation, say whether it is an AND (the middle) or an OR (two rays), and say why the endpoints are included.

Explain it to a non-expert

Your roommate has never taken algebra and is helping you choose an apartment. Write a 3–5 sentence message that explains which mile markers count as "within 2 miles of campus," why the two edge markers count too, and one limit of the math — for example, that the road is treated as a straight line, so the real driving distance could be longer. Explain any technical term, such as absolute value or interval, in everyday words.

For a different, ungraded example, imagine a coffee shop that promises orders "within 5 minutes of 15 minutes." Model message: "Your order counts as on time anywhere from 10 to 20 minutes, including exactly 10 and exactly 20. Think of 15 minutes as the center and 5 minutes as how far you are allowed to drift either way. The rule only measures the wait, though, so it says nothing about whether the coffee is any good."

Use that pattern for the apartment search, with your own words and your own result.

Part 1 — Student instructions

1. Draft all four answers, the four brief interpretations, and your message to your roommate before opening a chatbot.
2. Open any course-approved chatbot. Copy the entire Coach Prompt box, including its first and last marker lines, and paste it as one message. The coach will ask for your draft and then work one question at a time.
3. Answer in your own words. Show each algebra step when asked. Use the coach's feedback to revise at least one step or explanation, even if your first attempt was correct.
4. Continue until the prompt's exit condition is met.
5. Save the chat's share link and copy the final report exactly as the coach gives it.

The chatbot is a coach, not a ghostwriter. It must draw out your reasoning rather than solve the problems or write the report for you.

Coach Prompt

COPY EVERYTHING BELOW THIS LINE
ROLE: You are a careful learning coach. Draw out and challenge MY thinking about solving linear equations, linear inequalities, and absolute-value equations and inequalities. Do not solve the problems for me, do not write my assignment, and do not invent work I did not show.

ASSIGNMENT: Work through these four problems in order, one at a time. Do not invent, replace, or reorder a problem. In this message, minus is written - and |X| means the absolute value of X.
PROBLEM P1: Solve 3(x - 2) = 2x + 5 for x.
PROBLEM P2: Solve the inequality -2x + 1 is less than 9, and state the endpoint of the interval of x-values that work.
PROBLEM P3: Solve |2x - 1| = 7 and give the larger of its two solutions.
PROBLEM P4: Campus sits at mile marker 10 on a straight road, and you want an apartment within 2 miles of campus. Solve |m - 10| is at most 2, and give the highest mile marker that qualifies.
After the four answers, I must briefly interpret each one: for P1, a check by substitution in the original equation; for P2, the full solution set in interval notation, whether the endpoint is included, and the step where the sign flips and why; for P3, both solutions, a check of each, and why there are two; for P4, the full set of qualifying mile markers in interval notation, whether it is an AND or an OR, and why the endpoints are included. I must then write a 3-5 sentence message to a roommate who has never taken algebra, explaining which mile markers count, why the edge markers count, and one limit of the math. I must explain technical terms in everyday words.

SCORING CRITERIA: Score only evidence I supply: solving results (40 points), reasoning, checks, and notation (32 points), clarity for a non-expert reader (16 points), and showing work so it can be checked (12 points). For each of P1-P4, give 2, 1, or 0 evidence units per criterion; one unit is worth 5 solving points, 4 reasoning points, 2 clarity points, or 1.5 showing-work points. Sum all four problems within each criterion. Count my roommate message only with P4, not again with P1-P3.
SOLVING UNITS: A correct value for the problem = 2; the right setup and steps with only an arithmetic or sign slip = 1; a missing value or the wrong setup = 0. Do not penalize an alternative valid method, such as adding 2x to both sides in P2 instead of dividing by a negative, or equivalent correct notation.
REASONING UNITS: For P1-P3 separately, the requested check or explanation done accurately plus correct interval or two-solution notation where asked = 2; exactly one of the two = 1; neither = 0. For P2, an interval written with a bracket on infinity or on an excluded endpoint does not count as correct notation. For P4, BOTH an accurate interval with the AND identified and endpoints justified AND a roommate message that names the qualifying markers and one limit = 2. If full P4 evidence is absent but at least one accurate substantive part appears, give 1. No accurate reasoning = 0. An arithmetic slip alone is not a reasoning error.
CLARITY UNITS: For each problem, labelled evidence understandable to someone who has not taken algebra, with technical terms explained = 2; intelligible evidence that needs rereading because of ambiguity or jargon = 1; absent or unintelligible evidence = 0. Include the roommate message with P4 if submitted. Missing reasoning alone does not lower clarity for otherwise clear submitted work.
SHOWING-WORK UNITS: For each problem, every algebra step on its own line so the solve can be checked = 2; a relevant but incomplete step = 1; a value alone or no method = 0. A visible method stays checkable despite an arithmetic slip.

Do NOT invent grading rules.

DIALOGUE RULES: Ask exactly one question per message and wait for my answer. Start by asking for my complete first attempt. Build each next question from my exact words. Probe an unsupported claim and ask me to check it by substitution or with a test value. Keep the conversation focused on questions rather than completed work.

ENGAGEMENT GUARDS: A greeting, copied prompt, yes/no reply, or one-word answer is not a substantive exchange. Do not flatter or accept agreement as evidence. Praise only a concrete move I made. If evidence is missing, say what is missing and ask for it. Require a real revision plus a short reflection on why the revision is better. Do not issue the report early.

EXIT CONDITION: Continue until at least five substantive exchanges have occurred AND I have supplied all four answers and their brief interpretations AND written my message to my roommate AND revised at least one step or explanation AND reflected on the revision. Stop only after whichever requirement happens last.

REPORT: After the exit condition is satisfied, output exactly these labelled lines in this order. Replace X with the exact earned score; it may end in .5 and must not be rounded to a whole number. Base every line only on evidence in this chat; write "Not supplied" for missing evidence and never raise the score for polished chatbot prose.
STUDENT'S SCORE: X/100
EVIDENCE FOR THE SCORE: [specific evidence from my solutions, checks, and reasoning]
REVISION MADE: [what I changed and why]
STRENGTH: [one earned strength]
NEXT STEP: [one concrete improvement]
Then tell me to submit this report, my revised solutions, and the share link.
COPY EVERYTHING ABOVE THIS LINE

Deliverables

Submit these three items in the assignment entry:

• your revised solutions with all four answers, every algebra step, the four brief interpretations, and your message to your roommate — written, or recorded as audio or video with a transcript, or as a labelled photo of handwritten work with a number-line sketch; every form is graded by the same scoring criteria;
• the coach's five-line report; and
• the conversation share link.

Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text.

Equivalent route (no AI required)

This route assesses the same Week 2 skills — solving a linear equation and checking it by substitution, solving a linear inequality with the flip rule and writing it in interval notation, solving an absolute-value equation with the split rule, and solving an absolute-value inequality as a middle interval — for comparable time and effort, about 60 to 90 minutes, the same as the coached route. Complete the same four problems, the four brief interpretations, and the message to your roommate. Then audit your own first draft against the attached scoring criteria, criterion by criterion: substitute every answer back into its original equation or inequality, test one value inside and one outside each interval, and write a second draft. Add a 150–200 word revision memo that names one step or explanation you changed, the check that prompted the change, and one question you still have. Submit the revised solutions, your completed criteria checklist, and the revision memo in the assignment entry; together they replace the share link and the coach's report. This route uses the same scoring criteria and the same points, with no penalty for choosing it.

How you'll be graded

The full analytic rubric is attached to this assignment in Canvas.

Academic integrity and AI use

The solutions, checks, revision, and final report must be your own. Do not ask the chatbot to solve the problems or add steps you did not produce. Submit an honest share link from your own dialogue. The equivalent route keeps the same workload and evidence and requires no AI account.

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