Madison created this solved this proof. she wants to know if she solved it correctly. after looking at the proof, decide whether she solved the proof correctly. if she did not explain why it is incorrect and correct it. given : 4(5n + 7)-3n = 3(4n - 9) prove: n=-11 statements reasons 4(5n + 7) - 3n = 3(4n - 9) given 20n + 28 - 3n = 12n - 27 distributive property 17n + 28 = 12n - 27 simplify 5n + 28 = -27 addition property of equality 5n = -55 multiplication property of equality n = -11 division property of equality

madison correctly solved the equation, but step 3 should be subtraction property of equality.

work: to start off, madison correctly used the distributive property in step one. She also correctly simplified in step two. Step three is where she messed up. somehow, she put "Multiplication Property of Equality" when she actually used the subtraction property of equality. step 3 and step 4 were still correctly solved, though.

answer: f true

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!