4) Solve the equation below. You can type out your steps, record your steps or upload a picture of your steps. Make sure to show/explain every step as well as your final answer.

4(x - 5) - 2 = 56

4x-20=58

                   +20 +20

               4x=78

                /4  /4

                 x=19.5

Step-by-step explanation: Parenthesis first. Multiply 4 times x (which is 4x) and 5 times 4 (which is 20). So you get 4x-20-2=56. Move the (-2) over to the other side using inverse operations, making it 4x-20=58. Then move over the 20, again using inverse operations, making it 4x=78. Then isolate the variable by dividing both sides by 4 leaving you with x=19.5. You can check the work by plugging it in:

4(19.5-20)-2=56

78 - 20 = 58  (moved the -2 over to the other side)

58 = 58. That is true so the answer is correct.

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!