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Week 2 · Assignment: Traditional alternative (no AI)

Week 2 — Solve It, Check It, Explain It: Equations and Inequalities — Traditional alternative (no AI)

College Algebra Free sample edition
Traditional alternative (no AI), unpublished. In the course this is a separate assignment that ships unpublished beside the adaptive assignment: same objective, no AI. An instructor who prefers it publishes it and unpublishes or deletes the adaptive one, as the note at its top says.

Instructors: publish this instead of the adaptive version if you prefer, and unpublish or delete the adaptive one.

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 week you learned to solve a linear equation with one principle and four tactics, to flip an inequality sign when you divide by a negative number, to write a solution set in interval notation, and to solve absolute-value equations and inequalities as distances. 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. In this assignment you solve four problems, check each one, and explain one result to someone who has never taken algebra. This week's lecture tutorial, quiz, discussion, and Model/Build Studio practice the same ideas from other angles.

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.

Show your work. A reader should be able to follow every step from the original problem to your value without guessing which operation you used, and every check should show both sides evaluated.

Deliverables

Submit a single solutions report containing:

  • the four answers, each with every algebra step on its own line and the brief interpretation the task asks for;
  • your message to your roommate, explaining which mile markers count, why the edge markers count, and one limit of the math; and
  • a one-line check summary listing the value you substituted into each original problem and what each side came to.

Keep it to roughly one or two pages. Clear and correct beats long.

Choose how you show it. Present your report as written text, or as a recorded audio or video explanation of about three minutes 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. 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.

How you'll be graded

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

Academic integrity and AI use

This version is designed to be completed without AI: do the algebra, the checks, and the writing yourself, without a chatbot or other AI tool. You may use a calculator for the arithmetic or a graphing calculator such as Desmos to confirm a check. Submitting AI-generated work as your own, or copying another student's steps, is an integrity violation under the course policy.

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