Solving Linear Equations

A linear equation in one variable can be written in the form $ax + b = c$ with $a \neq 0$. The variable appears only to the first power — no $x^2$, no $\frac{1}{x}$.

The general strategy:

1. Simplify each side (expand brackets, collect like terms).
2. Move variable terms to one side, numbers to the other, using inverse operations on both sides.
3. Divide by the coefficient of the variable.
4. Check by substitution.

Worked example. Solve $3x + 4 = 19$.

Check: $3(5) + 4 = 19$ ✓

A second example with a real bill. A minibus taxi charges a R10 flag fee plus R8 per kilometre. A trip costs R50 — how far was it?

Translating a sentence into an equation and solving it is the whole game of algebra.