Question

CAN SOMEONE PLEASE HELP ME....
2|z+1|-3=z-2 solve

Answer 1

do you know what the "|" symbols around an expression mean?

Answer 2

absolute value

Answer 3

correct, so this means what ever appears between these symbols (positive or negative value), we just drop the sign of the result and just consider its magnitude.

agreed?

Answer 4

agreed

Answer 5

ok, so we can break these types of problems into two:

1. consider the case when the expression between the "|" symbols is positive
2. consider the case when the expression between the "|" symbols is negative

Answer 6

so lets take the 1st case, in this case (since the expression between the symbols is positive), the "|" can just be removed to give:

2(z+1) - 3 = z - 2

can you solve this to find z?

Answer 7

2z +2-3=z-2
2z-1=z-2
z=-1

Answer 8

perfect!

Answer 9

now lets look at the second case...

Answer 10

if the expression between the "|" symbols is negative, then taking its absolute value is the same as putting a minus sign in fron of it.

e.g. |-3| = -(-3) = 3

understand?

Answer 11

yup

Answer 12

great!

so that gives us:

2(-(z+1)) - 3 = z - 2

can you solve this to find z?

Answer 13

-2z+2-3=z-2
-2z-1=z-2
-1=3z-2
3z=1
z=1/3

Answer 14

almost - you made a sign error in the first step:

2(-(z+1)) - 3 = z - 2
2(-z-1) - 3 = z - 2
-2z -2 -3 = z - 2

Answer 15

-2z -2 -3 = z - 2
-2z-5=z-2
-5=3z-2
-3=3z
z=-1

Answer 16

perfect!

so you see there is only ONE solution to both cases: z=-1

hope you understood the process. :)

Answer 17

thank you very much!

Answer 18

yw :)