For any given journey, ABC Taxis charge customers a base fare of £5 plus 80p per mile. XYZ Taxis charge a base fare of £3 plus £1.20 per mile. Find the number of miles, x, that must be traveled in order for ABC taxis to be the cheaper journey option.

This question can represented in algebraic form:
ABC Taxis = 0.8x + 5XYZ Taxis = 1.2x + 3
Noting that the units must be consistent throughout the question, so we have changed the pence into miles. (80p = £0.8)
The question asks us to find out, for what values of x, ABC Taxis (0.8x +5) is less than (<) XYZ Taxis (1.2x + 3), i.e:
0.8x + 5 < 1.2x + 3
This can then be treated as a standard inequality. By subtracting 0.8x from each side of the inequality we arrive at:
5 < 0.4x + 3
We can then subtract 3 from both sides of the inequality:
2 < 0.4x
To isolate x, we must divide by 0.4 (equivalent to dividing by 4/10) leaving us:
5 < x
This tells us that ABC taxis overall fare will be cheaper for any distance, x, that is greater than 5.
(This can also be completed through graphical methods)