Where did this student make the mistake when solving this inequality? -2x - 3 > 5x + 4

-2x -2x

-3 > 3x - 5

+5 +5

2 > 3x

/3 /3 (divide by 3)

2/3 > x

Question 1 options:

2x needed to be added to both sides to move the entire term to other side of the inequality sign to combine like terms.

5 should have been subtracted from both sides of the inequality since I am combining like terms.

When dividing by 3 you need to switch the sign.

When subtracting 2x to both sided of the inequality, you should switch the sign.

answer: (1,3) and (-2,0) i think.

what is all that apply?

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!