solve: |2z - 3| = 4z - 1 and check for extraneous solutions.

Question

amistre64 · Answer

split it into 2 parts:

2z - 3 = 4z-1
       and
2z - 3 = -(4z-1)

amistre64 · Answer

weed out any z values that make 4z-1 go negative

anonymous · Answer

okay, did that. what next?

amistre64 · Answer

what values did you get?

anonymous · Answer

2z - 3=4z-1 and 2z-3=-4z+1

amistre64 · Answer

solve each one for z using algebraic techniques

anonymous · Answer

z = -1 and z=1.5

amistre64 · Answer

|dw:1344370383592:dw|i think graphically we have something akin to this

amistre64 · Answer

http://www.wolframalpha.com/input/?i=y%3D%7C2x-3%7C+and+y%3D4x-1 almost seen it correctly :)

amistre64 · Answer

4z - 1 > 0

4z > 1

z > .25

amistre64 · Answer

so the negative z can be discarded

anonymous · Answer

ok, but it says to check for extraneous solutions

amistre64 · Answer

2z - 3=4z-1      2z-3=-4z+1
     +3      +3          +3       +3
-----------      ------------
 2z = 4z + 2        2z = -4z + 4
-4z   -4z           +4z     +4z
------------    --------------
  -2z = 2               6z = 4
    z = -1                   z = 2/3

amistre64 · Answer

extraneous solutions are "false" solutions

amistre64 · Answer

when z=-1; we have a false statement, so we discard that as extraneous

anonymous · Answer

is the 2/3 extraneous too?

amistre64 · Answer

no

amistre64 · Answer

2/3 makes a true statement, therefore it is not a false solution

anonymous · Answer

ok thank you

amistre64 · Answer

yep

anonymous · Answer

ok, on this question the equation is: 7|8-3h|=21h-49

the first answer i got was: h=2.5 the second was: 0(zero)h=-1 what does that mean?

amistre64 · Answer

first divide off the 7

 7|8-3h|=21h-49
    /7            /7
----------------
  |8-3h| = 3h - 7

since |...| are always 0 are bigger; no negative values allowed

3h - 7 >= 0
     +7      +7
-------------
     3h >= 7
       h >= 7/3    anything less than 7/3 is useless to us

amistre64 · Answer

since |a| = n ; then |-n| or |n| = n

a = n or a=-n

|8-3h| = 3h - 7

8-3h = 3h - 7      8-3h = -(3h - 7)

amistre64 · Answer

8-3h = 3h - 7      8-3h = -(3h - 7)
-8              -8      -8                 -8
------------      ----------------
 -3h = 3h -15          -3h =-3h - 1
 -3h   -3h                +3h   +3h
-------------       --------------
   -6h = -15              0 = -1   , simply false
      h = -15/-6
      h =  5/2

amistre64 · Answer

is 5/2 >= 7/3  ??

amistre64 · Answer

since  5*3 >= 7*2
           15 >= 14  ; then yes;  h=5/2 is correct

amistre64 · Answer

not that i approve of "doing all the work"; but it just seems a better way to explain the process ....

anonymous · Answer

ok thank you again

anonymous · Answer

Ok sorry to bother you again but i don't know if i did this one right:

3|5t - 1| +9 < or = to 23

and my answers are:

t<or= to 3.54 and t>= -3.14