### Abstract

‘Linear equations and inequalities’ describes how to solve the simpler type of linear equations with one unknown and simultaneous linear equations with two unknowns. It also introduces manipulation of inequality signs, and closes with an example of finding the values of unknown quantities that satisfy particular equations while being constrained to lie within certain ranges. This mathematics underpins much of the logistics of modern society, governing operations such as railway and airline schedules, while allowing businesses to meet customer demand by running lower stock inventories, which represents an enormous and ongoing cost saving. The algebraic ideas of elimination and constraint satisfaction underlie all this.