contestada

The following is an indirect proof of the Division Property of Equality: For real numbers, a, b, and c, if a = b and c ≠ 0, then . Assume . According to the given information, a = b. By the Multiplication Property of Equality, one can multiply the same number to both sides of an equation without changing the equation. Therefore, . Through division, the c's cancel and ______. This contradicts the given information so . Which statement accurately completes the proof? a = b a ≠ b

Respuesta :

danielmaduroh
The statement above establishes the following:

If:
(1) [tex]a=b[/tex]
(2) [tex]c \neq 0[/tex]

Then we must assume that in fact [tex]a=b[/tex], therefore if we multiply the same number, say c, to both sides of an equation this one is not affected, then we have:

(3) [tex]ac=bc \rightarrow c(a-b)=0[/tex]

First answer.

Through division, the c's cancel and zero. Let's prove it:

a. If we divide (3) by c, this is canceled and the equation (3) is converted to:

[tex]a-b=0[/tex] All right up here

b. If we divide (3) by (a - b), this term is canceled and the equation (3) is converted to:

[tex]c=0[/tex] But this is a contradiction given that in the statement above [tex]c \neq 0[/tex] 

Second answer. Which statement accurately completes the proof?

The statement that completes the proof is necessarily: 

[tex]a \neq b [/tex]

For example:

[tex]a=5[/tex]
[tex]b=4[/tex]
[tex]c=9[/tex]

Given that:
[tex]a \neq b[/tex] and [tex]c \neq 0[/tex]

Then:

[tex]ac \neq bc \rightarrow 5\times9 \neq 4\times9 \rightarrow 45 \neq 36[/tex] 

Otras preguntas