Which property is illustrated by the equation? (2x + 1) + 3y = 2x + (1 + 3y)

Answers: Commutative Property of Addition, Identity Property of Addition, Associative Property of Addition, or Distributive Property of Addition.

Associative Property of Addition

Step-by-step explanation:

Associative Property of Addition - if the grouping changes, the answer will be the same - Correct (2 + 3) + 5 = 2 + (3 + 5)

Identity Property of Addition - anything added by 0 will equal itself (5 + 0 = 0, 2.3 + 0 = 2.3, etc.)

Commutative Property of Addition - if the order changes, the answer will be the same (2 + 3 = 5 and 3 + 2 = 5 also)

Distributive Property of Addition - allows you to "distribute" a number (2(3 + 5) = 2 * 3 + 2 * 5 = 6 + 10 = 16)

square

step-by-step explanation:

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!