Week 2 · Readings & resources

Week 2 — Readings & Resources

College Algebra Free sample edition

Your primary reading is Chapter 2 (in this module). Everything below is the optional, go-deeper layer — pick what helps, skip the rest.

How to use this page

This page has 12 items (6 readings and 6 videos). Allow 67–87 minutes for everything. Each group points back to the matching chapter section and class-session segment, so use the full menu when you want more practice, or take the quick path below.

Every video here has captions: turn them on with the CC button in the player. The chapter covers the same ideas in text.

Pick-one quick path (20–22 min total)

① How do I get x alone? Solving a linear equation and checking it

Chapter 2, Section “Solve a linear equation: one principle, four tactics” · Session 1, Segment 1, “Solving linear equations and checking them” · Remember: do the same thing to both sides, then put your answer back into the original equation.

Solving Linear Equations with One Variable — MathBootCamps — one goal, getting the variable alone by doing the same thing to both sides, worked from one-step equations up to one with parentheses on both sides, with a substitution check after each; the closing section matches the chapter's identities and contradictions, though it calls an identity infinitely many solutions where this course writes all real numbers. This builds on Week 1's work with the distributive property and combining like terms. (reading, 10–14 min)
Ex 1: Solve an Equation with Fractions with Variable Terms on Both Sides — Mathispower4u — one equation with fractions on both sides, solved by clearing the fractions first. (video, 5 min) (captions: creator)
Infinitely Many Solutions or No Solution? Equations Special Cases — Mario's Math Tutoring — what happens when the x terms cancel: a true leftover means every number works, and a false one means none does. (video, 3 min) (captions: automatic)

② Which way does the sign point? Linear inequalities and interval notation

Chapter 2, Section “Solve a linear inequality and write it in interval notation” · Session 1, Segment 2, “Linear inequalities and interval notation” · Remember: flip the sign when you multiply or divide by a negative, and infinity always gets a parenthesis.

Linear Inequalities — Math Hints — a table that sets inequality notation, interval notation, and a number line side by side, then two inequalities solved step by step, one of which divides by a negative and flips the sign; the page calls parentheses soft brackets and square brackets hard brackets. Read through the two solved inequalities and skip the compound inequalities at the end. (reading, 6–9 min)
Intervals — Math is Fun — the gentlest page on this list: an inequality, an interval, and a number line side by side, with open and closed ends and what to do with infinity. Stop here before using intervals to describe a function's inputs; next week takes that up. (reading, 4–6 min)
Ex: Solve a Linear Inequality Requiring Multiple Steps (One Var) — Mathispower4u — two multi-step inequalities, each answer written in interval notation. Use it while working through the Week-2 module overview. (video, 3 min) (captions: creator)
Solve linear inequality in interval notation Elem6 — YourMathGal — one more linear inequality solved and written as an interval, at a calm pace. (video, 4 min) (captions: automatic)

③ Why two answers? Absolute-value equations

Chapter 2, Section “Solve an absolute-value equation with the split rule” · Session 2, Segment 3, “Absolute-value equations” · Remember: absolute value is a distance, so split into two cases unless the right side is negative.

Absolute Value Equations — MathBootCamps — isolate the absolute value first, then split into two equations, with worked cases that end in two solutions, one solution, or none, and a number-line picture of why the split works; where the page says an absolute value is always positive, read never negative, since the absolute value of 0 is 0. (reading, 6–9 min)
Solving Absolute Value Equations - Example 2 — Patrick J — a short worked example of one absolute-value equation solved by splitting it into two cases. (video, 2 min) (captions: automatic)

④ The middle or the two rays? Absolute-value inequalities

Chapter 2, Section “Solve an absolute-value inequality: the middle or the two rays” · Session 2, Segment 4, “Absolute-value inequalities” · Remember: less than a distance is the middle, an AND; greater than a distance is the two rays, an OR.

Absolute-Value Inequalities — Purplemath — the less-than case and the greater-than case explained side by side, and why one gives a single interval while the other gives two pieces. (reading, 6–9 min)
Solving Absolute Value Equations and Inequalities - Number Line & Interval Notation - Algebra — The Organic Chemistry Tutor — many worked examples in a row, each answer drawn on a number line and written in interval notation, including cases with no solution. (video, 13 min) (captions: automatic)

Optional one-stop reference (free online reference)

Desmos Graphing Calculator — Desmos — the free graphing calculator this course uses all term. For this week, type both sides of an equation as two graphs and read where they cross, or type an absolute-value graph against a flat line to see the middle or the two rays; skip everything else for now. (reading, 5–10 min)

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell your instructor and use the reference above in the meantime.

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