Hich of the following expressions is equivalent to |x + 4| < 5? a. –5 > x + 4 < 5 b. –5 < x + 4 < 5 c. x + 4 < 5 and x + 4 < –5 d. x + 4 < 5 or x + 4 < –5 select the best answer from the choices provided a b c d

option B

Given : |x + 4| < 5

A. –5 > x + 4 < 5

B. –5 < x + 4 < 5

C. x + 4 < 5 and x + 4 < –5

D. x + 4 < 5 or x + 4 < –5

In general , |x|< n where n is positive

Then we translate to -n < x < n

|x + 4| < 5

5 is positive, so we translate the given absolute inequality to

-5 < x+4 < 5

So option B is correct

look a the sides they are perpendicular

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!