Solve the equation. Write a justification for each step.

2(x−4)=−4x+10

x = 3

Step-by-step explanation:

Start by distributing the 2:

2x - 8 = -4x + 10

Now bring all the terms with the x on the first side and all the terms without the x on the second side, them sum what you can sum:

2x + 4x = 10 + 8

6x = 18

We divide by 6:

x = 18/6 = 3

2x−8=−4x+10

2x=−4x+10+8

2x=−4x+18

2x+4x=18

6x=18

x = 18/ 6

x = 3

x = -2

y = 848

step-by-step explanation:

plug in the numbers

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!