Week 2 — Linear Equations & Inequalities

Welcome to your Week 2 Start Here page.

Why this matters

Finding every number that makes a statement true is how a nursing student keeps a dose in a safe range and how a small-business owner stays under budget.

In plain language

This week you learn to find the number that makes a statement true. Some statements have exactly one such number, and you find it by solving an equation (undoing what was done to the unknown, one step at a time, until it stands alone). Other statements are true for a whole range of numbers, like "spend at most 45 dollars," and you describe that range with an inequality (a statement that one side is smaller or larger than the other). You will also meet absolute value (how far a number sits from zero, whichever direction it lies), which turns "within 2 miles" into algebra. Every answer you find, you check by putting it back in.

• Already covered: Week 1, Real Numbers, Exponents & Algebraic Expressions, gave you the order of operations, the properties of real numbers, and the habit of distributing and combining like terms.
• This week: solving linear equations, identities and contradictions, linear inequalities and interval notation, and absolute-value equations and inequalities.
• How they connect: every solve starts by simplifying each side, and simplifying is exactly what Week 1 taught.
• Where we're going next: Week 3, Functions: Notation, Domain & Range, uses these solving moves to find which inputs a function allows.

Focus

How do you find every number that makes a statement true, and prove it? You solve, flip, and check.

By the end of this module, you should be able to:

• [ ] solve a linear equation and check it by substitution
• [ ] tell an identity from a contradiction
• [ ] solve a linear inequality, flipping on a negative, in interval notation
• [ ] solve absolute-value equations and inequalities as distances

To-do

Plan your week

1. Read Chapter 2 (about 35 minutes), then the lecture and slides.
2. Work the lecture tutorial (60–90 minutes) and the practice set (about 20 minutes).
3. Do the Model/Build Studio (about 90 minutes), the discussion, and the assignment.
4. Take the quiz.

This week's checkpoint: solve −3x > 9, write it in interval notation, and test one value.

You've got this

Take it in order, and ask your instructor if a step snags.

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