Which algebraic expression is equivalent to the expression below?

9(x - 6) + 11(x + 12)

a.
99x + 78

b.
20x + 5

c.
20x + 78

d.
20x + 186

Hey there! :)

To find out which algebraic expression is equivalent to our given expression, we must simplify everything out.

9(x - 6) + 11(x + 12)

Simplify by using the rainbow method. This just rids us of our parenthesis.

(9 · x) + (9 · -6) + (11 · x) + (11 · 12)

Simplify!

9x + (-54) + 11x + 132

Add like terms.

(9x + 11x) + (-54 + 132)

Simplify.

20x + 78

So, our equivalent equation is C. 20x + 78

~Hope I helped!~

C) 20x+78

Step-by-step explanation:

9(x-6)+11(x+12)

9x-54+11x+132

20x-54+132

20x+78

b) 36

step-by-step explanation:

18 times 2 is 36

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!