NapkinCalc

Pre-Algebra — Numbers & First Variables

A first look at variables

continues from lesson 4 — values defined earlier in the course stay live here

ELI5: a variable is a letter standing in for an unknown number — the single idea that turns arithmetic into algebra. "Three more than twice a number" becomes 2x + 3, and you can evaluate it for any x. At x = 5 it's 2·5 + 3 = 13.

twiceplus3(x)=2⋅x+3twice_{plus3}\left(x\right) = 2 \cdot x + 3 a rule written with a variable
atfive=twiceplus3(5)at_{five} = \mathrm{twice_{plus3}}\left(5\right) = 1313 evaluate it at x = 5: 13
✓ pass atfive==13at_{five} == 13 the variable rule, run on a number

Real-world hook: variables are how a formula works — area = length × width, distance = speed × time — one rule that handles every set of numbers you plug in.

Try it yourself: evaluate 4x − 1 at x = 6.

evalyou=4⋅6−1eval_{you} = 4 \cdot 6 - 1 = 2323 ✏️ Your turn: plug x = 6 into 4x − 1 (so 4·6 − 1).
✓ pass abs(evalyou−4⋅6−1)<10−9\mathrm{abs}\left(eval_{you} - 4 \cdot 6 - 1\right) < 10^{-9} green when you evaluate the expression correctly

Where next: Algebra 1A turns these variables into equations you can solve.