Equations » What is an equation?

Important:

Make sure you know what a formula is first and how to work with it.

What is an equation?

– A formula where the outcome is filled in.
– Two formulas with a =-sign in between.

Examples

3x + 5 = 8
7x + 4 = 9x2 – 5x

Mathematically said:
An equation is a mathematical statement that asserts the equality of two expressions, with one or more unknown variables.

Equations can only be solved when they have one unknown variable.
Of course there are exceptions:

– When you can get rid of variables by reducing the equation to a point where you have just one variable left.
– Substitute variables with formulas based on one of the other variables.

Where are equations used for?

With an equation you can calculate 'in reverse' with formulas.
When you only know a formula and the outcome of the formula, you can calculate by making and solving the equation which value had to be filled in into the formula to get that outcome.

Example 1

A company calculates the tariff for a job with the formula a = 25n + 15 (With a the amount in euros and n the number of hours worked).
What if you get charged 127.50 euros and you want to calculate how many hours they have worked.
You can make and solve the equation 127.50 = 25n + 15. You can calculate with that equation that n = 4.5 hours.

Example 2

The height h in metres after t seconds of a ball being kicked can be calculated using the formula h = –0,5t2 + 5t.
If you want to know how many seconds it takes for the ball reaches the ground again,
you can solve the equation: 0 = –0.5t2 + 5t (you fill in zero for the height).
Solving this gets you after t = 10 seconds.
If you want to know after how many seconds the ball is at an height of 12 metres,
you can solve the equation: 12 = –0.5t2 + 5t (you fill in twelve for the height).
Solving this gets you t = 4 and t = 6 seconds.

How do I solve an equation?

Look at the other pages of equations to see how you can recognise and solve certain equations.