The Language of Equations
An equation is not a puzzle set by an enemy. It is a sentence – 'this amount is the same as that amount' – written compactly enough to be checked. This chapter teaches the reading knack: what the letters stand for, why the two sides must balance, and the single rearranging move that turns one known fact into three usable recipes.
Intro: the confession that symbols scare people off, and the counter-claim – d = v × t contains nothing the reader didn’t already know from every car journey they have taken.
2.1Letters are nouns wearing small clothes
d, v and t are abbreviations for measured things – distance, speed (velocity, formally, from ch4), time – chosen so a fact fits on one line. Reading an equation aloud in full sentences, as this course will do every time a new one appears.
2.2The two sides balance
The = sign is a promise: whatever is on the left is the same amount as whatever is on the right. Consequence: do the same thing to both sides and the promise survives – which is the entire theory of rearranging, and the figure’s job to make bodily obvious.
2.3One fact, three recipes
d = v × t rearranged for t, then for v – slowly, both sides shown at every step, once and never again this slowly. The payoff named honestly: this one move is most of the algebra the seven courses will ever ask for.
2.4Graphs: equations you can look at
A graph is an equation with the numbers poured back in: every point a (time, place) pair, the shape of the line the personality of the motion. How to read axes before chapter 4 asks the reader to read slopes. No figure here – chapter 4’s grapher is the real classroom; this section just hands over the vocabulary.