Javon plays on the bunker hill basketball team and coach jones sets a goal for him to average a minimum of 18 points per game in his first six games. if he scores 20, 17, 14, 18, and 19 in his first five games, what must he score in his sixth game to average at least 18 points per game (express your answer as an inequality)?

If he does average exactly 18 points per game in the first 6 games, then his TOTAL points in those 6 games will be (6 x 18) = 108 points.

In his first 5 games, he has (20 + 17 + 14 + 18 + 19) = 88 points so far.

In order to total 108 for 6 games, he has to score (108 - 88) = 20 points in the 6th game. If he scores more than that, then his average for the 6 games will be more than 18 points per game.

In order to meet the goal that Coach Jones has set for him, Javon must score 20 points or more in the next game. S ≥ 20 .

This might scare Javon ... he has to equal or beat his best performance of the last 5 games.

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!