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What you will learn in Algebraic Expressions & Equations
1. Variables, Terms and What a Letter Means
A letter is a placeholder, and which kind of placeholder depends on where it appears — an unknown to find, a quantity that varies, or every number at once.
2. Expressions: Collecting, Expanding, Substituting
Terms combine only when they measure the same thing, which is why 3x + 2 is already as short as it gets.
3. Algebraic Identities as Areas
Every product of two brackets is a rectangle cut into pieces — and the missing middle term of (a + b)² is two of those pieces.
4. Linear Equations in One Variable
Solving is a sequence of operations applied to a whole equation, not a rule about moving letters across an equals sign.
5. Translating Words into Algebra
Two translations bracket every word problem: the situation into an equation, and the solution back into an answer to the question asked.
6. Linear Inequalities and Solution Regions
An inequality is answered by a region rather than a value, and multiplying by a negative reverses it.
7. Rearranging Formulae
Changing the subject of a formula is the same balance rule applied to letters — and it is the algebra Physics and Chemistry use most.
8. Absolute Value Equations and Inequalities
Read as a distance, the two cases of an absolute-value problem are the two directions rather than a rule to remember.
9. Linear Equations in Two Variables
With two unknowns and one equation the answer is a set of pairs, and that set is a straight line.
10. Simultaneous Equations: Algebra and Geometry
Two equations, two lines, one intersection — unless the lines are parallel, or the same line twice.