01Why this matters
A single expression can describe many situations. Instead of writing a new calculation for each ticket count, use a variable for the count.
02See it
03Understand it
A variable is a symbol that stands for a number. An expression combines numbers, variables and operations without asserting an equality.
In 3x + 2, x is the variable, 3 is its coefficient and 2 is a constant. The notation 3x means 3 × x. An equation such as 3x + 2 = 14 adds a statement that two expressions have equal values. Define what your variable means, including its unit if relevant.
04Guided example
A bike hire costs $5 to start and $4 for each hour h. Write its cost and evaluate it for 3 hours.
- The fixed part is 5, regardless of hours. The changing part is 4h.
- Combine them into C = 5 + 4h, where C is the cost in dollars.
- For h = 3, C = 5 + 4 × 3 = 5 + 12 = $17.
05Try it
06Practise it
07Use it in the real world
For n identical $2 notebooks, the cost expression is 2n dollars. If postage adds $6 once, the total becomes 2n + 6.
Go a little deeper
An expression’s allowed inputs form its domain. A ticket count usually uses non-negative whole numbers; measured time may include fractions.
08Quick check
09Summary
A variable is a symbol that stands for a number. An expression combines numbers, variables and operations without asserting an equality. For h = 3, C = 5 + 4 × 3 = 5 + 12 = $17.
Before moving on, explain the worked example in your own words. Use the hint on any question you want to revisit.
10Key idea
C = 5 + 4h
C is cost in dollars; h is time in hours; 4 is a rate in dollars per hour.
h = (C − 5)/4
Find this in the formula library →