Why this chapter matters
Linear equations describe break-even points, missing measurements, rates, and many other situations where one unknown must be found.
What you will learn
- Solve multi-step equations and verify solutions by substitution.
- Recognize equations with one, none, or infinitely many solutions.
- Solve and graph inequalities while handling negative multiplication correctly.
Lessons in this chapter
- Solving linear equationsUse inverse operations and preserve equality at every step. Read the full guide →
- Variables on both sidesCollect variable terms and diagnose identities or contradictions.
- Solving inequalitiesReverse the inequality when multiplying or dividing by a negative value. Read the full guide →
- Modeling constraintsTranslate limits such as budgets and capacities into inequalities.
Study task
Model a $120 event budget with a $30 room fee and $8 per guest. Find and graph the possible number of guests.
Chapter checkpoint
Solve 4(x - 2) + 3 = 2x + 9.
Expand to 4x - 5 = 2x + 9, subtract 2x, add 5, and get 2x = 14, so x = 7.