Question 156077: How do i solve the following inequalities and then graph it.
1. -2|x+1|>_-8
(the symbol before -8 is 1 greater or equal to)
2. 3(2x+8)<36
3.12>_-3x-6>3
4.5x-2<3x-8
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! solve the following inequalities and then graph it.
1. -2|x+1|>=-8
Divide both sides by -2 to get:
|x+1| <= 4
Solve the EQUALTIY:
x+1 = 4 or x+1 = -4
x = 3 or x = -5
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To solve the INEQUALITY:
Draw a number line and plot x = -5 and x = 3 on it
Check a test value from each resulting number-line interval to find solutions:
Let x = -10; you get |-10+1| <= 4; false, so no solutions in (-inf,-5)
Let x = 0; you get |0+1| <= 4; true, so solutions in (-5,3)
Let x = 5; you get |5+1| < 4; false, so no solutions in (3,+inf)
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Final Answer: [-5,3] or {x} -5 <= x <= 3}
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2. 3(2x+8)<36
(2x+8) < 12
2x < 4
x < 2
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3. 12>= -3x-6 >3
18 >= -3x > 9
-18 <= x < -3
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4.5x-2<3x-8
2x < -6
x < -3
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Cheers,
Stan H.
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