Introducing Algebraic Expressions

≈ 25 min

In algebra a letter stands for a number we may not know yet — a variable. An expression combines letters and numbers with operations but has no equals sign, so it cannot be solved; it can only be written, simplified or evaluated.

'Five more than a number $n$ ' is written $n + 5$ .
'Double a number $x$ , then add $3$ ' is written $2x + 3$ . Note $2x$ means $2 \times x$ .

To evaluate (substitute), replace the letter with a value:

3a + 2 \text{ when } a = 4: \quad 3(4) + 2 = 12 + 2 = 14.

Exam checkpoint

An expression is a mathematical phrase with no equals sign. A letter is a placeholder for a number, and $3x$ means $3\times x$ . Read each part: coefficient, variable and constant. Substitute carefully by putting the chosen value into brackets before you calculate.

Short worked example. If $x=4$ , then $3x+2=3(4)+2=14$ . The brackets make it clear that 3 multiplies the entire value of $x$ .

How do you write '7 less than a number $x$ ' as an expression?

$7 - x$

$x - 7$

$x + 7$

$7x$

Evaluate $3a + 2$ when $a = 4$ .

A loaf of bread costs R14, so $n$ loaves cost $14n$ rand. What is the cost (in rand) when $n = 6$ ?

Write an expression for 'double a number $x$ , then add $5$ '. Use the form like 2x+5.