Kaitlin is going to rent a truck for one day. there are two companies she can choose from, and they have the following prices: company a charges a fixed fee and allows unlimited mileage. company b has an initial fee and charges an additional fee for every mile driven. for what mileages will company a charge less than company b? use for the number of miles driven, and solve your inequality form.

Step-by-step explanation:

According to the information given in the statement, there are the following mathematical expressions:

Where

Considering

Then

The last equation means that to maintain the [text]priceB[\text] lower than [text]priceA[\text], the amount of driven mileage must be less than  . If [tex]x[\tex] becomes greater than the fraction, then the [text]priceA[\text] will be lower than [text]priceB[\text].

[tex]\frac{K - L}{A} < x \\ K - L < Ax \\ K < L + Ax[\tex]

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!