# Linear Equations

In this chapter, you will solve equations using the balance method and determine the formula for linear graphs.

theory
Balance Method
Take a look at the equation: 2x - 6 = 8
This equation states that 2x - 6 should have the value 8 . Solving the equation means you have to find the value for x that makes this equality true.
You can simplify the equation step by step, applying the same operation on both sides. This way the equation remains balanced, like a pair of weighing scales.
 2x - 6 = 8 Add 6 to both sides 2x - 6 + 6 = 8 + 6 2x = 14 Divide both sides by 2 2x ÷2 = 14 ÷2 x = 7
The above equation is true for x = 7 .

## Exercise 1

Solve these equations using the balance method.

a
b
c
practice
example
Writing linear functions
A new candle is 30 cm long. One burning hour reduces the height by 1.5 cm.
a
Write this as a mathematical function f(t) , where t is time in hours.
Solution: f(t) = 30 - 1.5 \cdot t
b
What is the height of the candle after 5 hours?
Solution: f(5) = 30 - 1.5 \cdot 5 = 30 - 7.5 = 22.5 cm
c
After how many hours has the candle burnt out?
(click on a step for details)

## Exercise 2

Try to find the function values for the given x . We have already filled out some solutions in the table as example.