Question 67442: Hello, I need help in solving the following compound inequalities. Thank you for your assistance.
1. x <= 0 and x + 6 > 3
2. |2x - 5| <= 0
3. -x > 0 or x + 2 < 7
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Hello, I need help in solving the following compound inequalities. Thank you for your assistance.
1. x <= 0 and x + 6 > 3
X+6>3
X>3-6=-3................OR ..............-3
BUT X<=0.....................................2
HENCE X LIES BETWEEN -3 AND 0....X=(-3,0]
-3
2. |2x - 5| <= 0
|ANY NUMBER|>=0 HENCE IT IS NOT POSSIBLE TO HAVE |2X-5|<5
BUT |2X-5| CAN EQUAL ZERO..HENCE
2X-5=0
2X=5
X=5/2
3. -x > 0 or x + 2 < 7
-X>0.....X<0........................1
X+2<7
X<7-2=5
X<5.......................................2
C0MBINING 1 & 2,WE HAVE
X<0
X=(-INFINITY,0)
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