• To solve linear equations. • To solve quadratic equations by factorisation and using the quadratic formula. • To model and solve word problems leading to linear and quadratic equations.
Introducing equations
An equation is a mathematical statement with two sides. An equation consists of a left-hand side (LHS) and a right-hand side (RHS) with an equality sign (=) between the sides.
Equation: LHS = RHS
Solving an equation means fi nding the values of the unknown quantity (variable) which make the statement true.
Example: 3x + 2 = 5 LHS
RHS
The value of 1 for x (the unknown value) makes this statement true. The value 1 for x that makes the statement true is known as a solution or root of the equation. The process of fi nding the solutions of an equation is known as solving the equation.
An equation behaves like a balance. Whatever you do to one
side, you must do to the other side to maintain equilibrium.
When you solve an equation, you should substitute the values obtained back into the original equation to check whether or not they make the statement true. Only those values that satisfy the original equation are acceptable solutions (roots).
The basic technique for solving all equations: Whatever operation you do to one side of an equation, you must do exactly the same operation to the other side of the equation.
