Question

Using complete sentences, write an indirect proof proving that if x = 40, then 5 over 6x − 3 ≠ 22.

Answer 1

use a proof by contradiction where if \[x \neq 40 \] then \[\frac{ 5 }{ 6x - 3 } = 22\]

Answer 2

hm.. im actually not 100% sure but this is what i would do...


forgot to mention that there is a unique solution such that \[x \in Z\] that satisfies that equation if you negate the statement
so you solve for x
5 = 22(6x - 3)
5 = 132x - 66
71 = 132x
x = 0.53 but 0.53 is not an integer solution so we have a contradiction here
thus if x = 40 then \[\frac{ 5 }{ 6x - 3 } \neq 22\]

Answer 3

woah I am so confused

Answer 4

indirect proof also means a proof by contradiction so you must prove that there is something wrong when you do the opposite of the problem

Answer 5

oh okay so complete sentences would be,

Lets say that we switch it around and do x≠40 instead of x≠22. We will do 5 over 6x-3=22 and solve for x. The answer is not an integer solution so we have a contradiction here, thus if x = 40 then.

Answer 6

actually i found an easier way when you negate the statement it becomes

if \[x \neq 40 \] then \[(\exists x \in Z : \frac{ 5 }{ 6x - 3 } = 22) \] The parenthesis is suposed to be curly brace

so that means if x = 1 then \[\frac{ 5 }{ 6(1) - 3 } = 22\]
but you get 1.667 which does not equal 22 so you have a contradiction and the proof is done

Answer 7

or then again what i said the first time works better

Answer 8

because it shows that the unique solution is not an integer solution

Answer 9

Thank you so much

Answer 10

your welcome

Answer 11

so what's the answer then?