Question

For what value of x is this inequality |x – 6|< - 8 true? Why?


help please i need some reason why??

Answer 1

why is it true ??

Answer 2

i think the answer is -2<x<14

Answer 3

why??

Answer 4

i need some reason there cause it is a problem solving.. :)

Answer 5

absolute value can never be less than 0 (negative)

so |x – 6|< - 8 is never true

Answer 6

lx-6l < -8
-8< x-6 < 8
-8 + 6 < x < 8 + 6
-2<x<14

Answer 7

actually my asnwer there is false but my prof. ask if true then why??

Answer 8

be definition absolute value means distance.
define distance,
can distance be negative ?

Answer 9

here's my answer..

Reason: there's no value for X and There is no solution to this problem. The left hand side is an absolute value which will always be positive no matter whether x is negative, zero or positive. But the right hand side is negative. A positive number can never be less than a negative number. So there is no value of x for which the inequality will be valid.

Answer 10

looks good

Answer 11

oh i forgot the negative sign in 8. My bad, so yeah you are right. the answer is no solution or null set because it will always be greater than or equal to 0

Answer 12

heheheh thanks folks :)

Answer 13

np :)

you may simplify the inequality if u want before giving it to ur prof

Answer 14

how?

Answer 15

|x – 6|< - 8

|x-6| + 8 < 0

min value of left side is 8, occurs at vertex when x = 6.
8 > 0

somehting like that may be.. but your justificaiton sounds solid. so dont bother...

Answer 16

heheheh ok :D