Which of the following is equivalent to |x - 2| = 6?


answer is: third given choice, is:

" x – 2 = 6 ; or; x – 2 = -6 "
___________________________
here how solve problem:
[of following] equivalent |x - 2| = 6?
______________________________________...
need read question--carefully: "which of following--is "equivalent" to...[an **absolute
value equation***].


then, knowing much, need @ answer choices given. given 4 (four) answer choices)---one of "none of above". given first 2 answer choices, different, , third answer choice includes correct choice of "either answer choice 1 --or answer choice 2".
______________________________________...
knowing this, know "none of above" possibility. know "choice 1" possible; , "choice 2".

however, here's tricky part: if determine either choice 1 or choice 2 correct, need examine other remaining choice see if correct, well. if, in fact, other correct, too, then, "answer choice 3" correct. if not, stick "original" choice 1 or choice 2.

important in case of "absolute value equation"; , word "equivalent.
______________________
know "total value" of "(x – 2)" can equal 6 when total value of "(x – 2)" either positive or negative. know because of bars representing "absolute value of (x – 2)" equalling 6.

thus, equivalent of |x – 2| = 6 occurs in case of either

case 1:

-(x – 2) = 6

or:

case 2:

(x – 2) =6 .
_________________
case 1:

-(x – 2) = 6 ---> can simplified ---> using foil method--pretend there "negative one"--->or, re-write as:

-1(x – 2) = 6 --->

-x + 2 =6
_____________
case 2:

re-write as:

x – 2 = 6
______________________________
now, in "case 2" scenario, same "answer choice 1".

thus, can rule out, "answer choice 4--none of above"---as "answer choice 2: "x – 2 = -6",
___________________________
now, remaining answer choices could "answer choice 1" or "answer choice 3".
_________________
have determine if "answer choice 3" correct"

going "answer choice 3"---we see "answer choice 3" states:

"x – 2 = 6 or x – 2 = -6 "
______________________________________...

remember question: either of these (above equations given in "answer choice 3")
equivalent to:

|x - 2| = 6 ??
__________________
know, "case 2" scenario above, "x – 2 = 6" equivalent.

need determine whether "x – 2 = -6 " equivalent, well. if so, "answer choice 3" correct. if not, "answer choice 1" correct.
______________________________________...
determine whether: "x – 2 = -6 " equivalent, well---we should go "case 1" scenario above.

in "case 1" scenario above, have: "-x + 2 = 6". so, need determine whether equivalent "x – 2 = -6 ". if so, "answer choice 3" correct solution entire problem.

"case 1" above, have: "-x + 2 = 6." equal to: "x – 2 = -6 " ??

since, "case 1", have "6" on 1 side of equation, can multiple entire equation "-1" "-6" on 1 side of equation, , can see appears on other side. can determine if "case 1" equation equivalent "x – 2 = -6 " :

-1 [-x +2 = 6 ] ---> x – 2 = -6 --->yes, exact equivalent!
______________________________________...
such, "case 1" equivalent "case 2",
, thus, correct answer is:

third answer choice: "x – 2 = 6" ; or, "x – 2 = -6" ; both equivalent to: |x - 2| = 6.

which of following equivalent |x - 2| = 6?answer x – 2 = 6
x – 2 = -6
x – 2 = 6 or x – 2 = -6
none of above


Science & Mathematics Geography Next



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