Question

Solve and find the solution set of:

II x-2 I + 4 = 8


> note: this is about EQUATIONS AND INEQUALITIES INVOLVING THE ABSOLUTE VALUE

Answer 1

when x is +ve,
x-2+4=8
x+2=8
x=6

when x is -ve,
-x+2+4=8
-x+6=8
-x=2
x=-2

Answer 2

so x = 6
x = -2

Answer 3

or could it be

x=-10
x=14
???

Answer 4

i'm confused...

Answer 5

I x-2 I + 4 = 8
| x-2 | = 4
x = 6
(when +ve)

I x-2 I + 4 = 8
| x-2 | = 4
x =- 2
(when -ve)

Answer 6

why yu r confused ?

Answer 7

because there are two bars

Answer 8

oh yeah.. there's a bar after 4 --- i forgot to add that

so the given is now:
II x-2 I + 4 I = 8

Answer 9

Ix-2I+4>0

Answer 10

what is the result?

Answer 11

\[\color{red}{|x-2|+4=8.}\]

\[\color{blue}{case-I}\]\[\color{purple}{x-2}+4=8.\]\[\implies x=8-4+2=6.\]
\[\color{blue}{case-II}\]\[\color{purple}{-(x-2)}+4=8.\]\[\implies -x+2+4=8 \implies -x=8-4-2=2.\]\[\implies -x=2 \implies x=-2.\]So; \[\color{green}{x=6\space and -2.}\]

Answer 12

Sol. for ur first question
second one is also easy
just concentrate on concept that
|a| = a ; if a>0
-a ; if a<0

Answer 13

For ur actual question;
case- I
+[(x-2)+4]=8

case-II
+[-(x-2)+4]=8.

case-III
-[(x-2)+4]=8.

case-IV
-[-(x-2)+4]=8.

\[\huge{\text{Solve these on ur own.}}\]

Answer 14

there will be 4 solutions.

Answer 15

Any doubt?

Answer 16

If yes then tell actual doubt:)