solve (2x + 1)(x -3)(x +7)<0
Nikki57:
before zero is it = sign
no
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(2x+1) * (x -3) * (x+7) < 0
Either two factors are positive and one negative, OR all three factors are negative. There are 4 cases.
case 1)
2x+1 > 0, x - 3> 0 AND x+7 < 0
ie., x > -1/2, x > 3, AND x < -7
NOT POSSIBLE.
case 2)
2x+1 > 0, x+7 > 0, AND x-3 < 0
ie., x > -1/2 , x > -7, AND x < 3
So -1/2 < x < 3
case 3)
2x +1 < 0 , x+7 > 0, x - 3 > 0
ie., x < -1/2 , x > -7 AND x > 3
NOT POSSIBLE
case 4)
2x+1 <0, x-3 < 0, x+7 < 0
ie x < -1/2 x < 3 , x < -7
So for x < -7
====
Finally the answer:
x < -7 or -1/2 < x < 3
x ∈ (-∞, -7) U (-1/2, 3)
Either two factors are positive and one negative, OR all three factors are negative. There are 4 cases.
case 1)
2x+1 > 0, x - 3> 0 AND x+7 < 0
ie., x > -1/2, x > 3, AND x < -7
NOT POSSIBLE.
case 2)
2x+1 > 0, x+7 > 0, AND x-3 < 0
ie., x > -1/2 , x > -7, AND x < 3
So -1/2 < x < 3
case 3)
2x +1 < 0 , x+7 > 0, x - 3 > 0
ie., x < -1/2 , x > -7 AND x > 3
NOT POSSIBLE
case 4)
2x+1 <0, x-3 < 0, x+7 < 0
ie x < -1/2 x < 3 , x < -7
So for x < -7
====
Finally the answer:
x < -7 or -1/2 < x < 3
x ∈ (-∞, -7) U (-1/2, 3)
please tell
it means that x can be in two ranges, - infinity to -7.. or it can be in between -1/2 to 3...
what ismeaning of " - infinity?"
if x is -10, -100, -0.4, -0.1, 0, 2, 1 , 2.9 ... for all these values, the given inequality is valid
infinity means the largest possible value..like value greater than any number.
thanks alot
you have to solve systematically like i did for inequalities... otherwise it is confusing..
mark as brainliest
thanks sir
hmmm
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