SOLUTION: What are the steps in solving this? | 2v - 1 | less than or equal to 9. Note: I don't know how to do the symbol for less than or equal to on my ipad.

Algebra ->  Absolute-value -> SOLUTION: What are the steps in solving this? | 2v - 1 | less than or equal to 9. Note: I don't know how to do the symbol for less than or equal to on my ipad.      Log On


   



Question 835204: What are the steps in solving this? | 2v - 1 | less than or equal to 9. Note: I don't know how to do the symbol for less than or equal to on my ipad.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+abs%28+2v+-+1+%29+%3C=+9+
-----------------------
Anything that you take the absolute value of will
be +0+ or a positive number, so
you know that the range of the left side
is +0+ to 9 inclusive
-------------------------
+0+%3C=+abs%28+2v-1+%29+%3C=+9+
I can say:
(1) +0+%3E=+2v+-+1+%3E=+-9+
and
(2) +0+%3C=+2v+-+1+%3C=+9+
==================
(1) +2v+-+1+%3C=+0+
(1) +2v+%3C=+1+
(1) +v+%3C=+1%2F2+
and
(1) +2v+-+1+%3E=+-9+
(1) +2v+%3E=+-8+
(1) +v+%3E=+-4+
-------------------
(2) +2v+-+1+%3E=+0+
(2) +2v+%3E=1+
(2) +v+%3E=+1%2F2+
and
(2) +2v+-+1+%3C=+9+
(2) +2v+%3C=+10+
(2) +v+%3C=+5+
-------------------
Rearranging the conditions:
(1) +v+%3C=+1%2F2+
(2) +v+%3C=+5+
and
(1) +v+%3E=+-4+
(2) +v+%3E=+1%2F2+
------------------
The controlling conditions are:
+-4+%3C=+v+%3C=+5+