SIMPLE EQUATIONS

CONTENT

1. Meaning of Equation
2. Solving Simple Equations
3. Translation of Word Problems into Equations and Vice Versa
4. Word Problems

Meaning of Equation

A sentence or statement says something about numbers written in symbols. Consider, for example, the statement: “I think of a number, I then triple it and add \(4\) to it”. We proceed as follows to write the statement in symbols. Let the number thought of be “\(r\)”, tripling it gives “\(3r\)”, and by adding \(4\) we get “\(3r + 4\)”.

If the result of this process is \(16\), then we have \(3r + 4 = 16\).

This symbolic expression is called a simple equation, with one unknown quantity, \(r\). The expression contains two sides referred to as the left-hand side, \(3r + 4\), and the right-hand side \(16\). The symbol ‘\(=\)’ is called the equality sign, which tells us that what is on the right-hand side is the same as what is on the left-hand side.

Solving Simple Equations

Examples:

Solve the following equations:

(i) \(x + 8 = 12\)

(ii) \(72 = 9x\)

(iii) \(\frac{x}{2} = 5\)

(iv) \(6 = \frac{1}{5}x\)

(v) \(x -4 = 18\)

Solutions:

(i) \(x + 8 = 12\)

The unknown \(x\) is on the LHS

Since \(8\) is added to \(x\) on the LHS, then we subtract \(8\) from both sides.