2.3 Expressions and formulae

Within one statement, repeated occurrences of the same letter represent the same value unless the letter is explicitly redefined.

The context may restrict possible values: a length is non-negative, a count is an integer, and a denominator cannot be zero.

Write numerical coefficients first and letter factors in a consistent order. Multiplication is implied by adjacency, but addition and subtraction remain explicit.

Use $=$ only between expressions known to have equal value. An expression such as $3x+2$ does not need an equals sign by itself.

If $T=5m-6n$, $m=4.2$ and $n=-2.5$, then $T=5(4.2)-6(-2.5)=21+15=36$.

For fractional values, keep exact fractions until the end when practical. Brackets also distinguish $(-3)^2$ from $-3^2$.

Potatoes cost 2 dollars per kg and carrots 3 dollars per kg. Buying $p$ kg and $c$ kg gives total cost $T=2p+3c$.

Define every symbol, match coefficients to their quantities, and test the formula with a simple numerical case and dimensional units.

Alisa picks $C$ cucumbers, Jena picks $C-5$, and Mikael picks $2C$. Therefore $T=C+(C-5)+2C=4C-5$.

For a perimeter, include every side before collecting; for area or volume, multiply the relevant dimensions. State the final subject explicitly, such as $T=\ldots$.

From $d=g+2ac$, subtract $g$ to get $d-g=2ac$, then divide by $2c$: $a=(d-g)/(2c)$, where $c
e0$.

Undo operations in reverse order. If necessary, clear a fraction first, but multiply every term on both sides consistently.

If $y=\sqrt{(x+1)/(x-4)}$, then $y^2(x-4)=x+1$. Collecting gives $x(y^2-1)=4y^2+1$, so $x=(4y^2+1)/(y^2-1)$, where the formula is defined.

For an even power, both roots may be needed unless the context restricts the subject, such as a positive length. A stated condition like $n>0$ selects the positive root.