I have to solve this inequality and then graph the solution

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  -8 < r ≤ 3

Step-by-step explanation:

Divide by the coefficient of r. It is negative, so the comparisons will be reversed.

  24/-3 < r ≤ -9/-3

  -8 < r ≤ 3

The < has no "or equal to" as a part of it, so the number -8 is not in the solution set. There will be an open circle on the graph at that point.

The ≤ includes the "or equal to" case, so the number 3 is in the solution set. There will be a solid dot on the graph at that point.

The line is shaded between the two dots, because values in between -8 and 3 are part of the solution set.

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!

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