SOLUTION: I need assistance solving these inequalities. Thank you! --- {{{ (x/5)-6<=-(x/2)+6 }}} --- {{{ x^2-x-6<0 }}} --- {{{ 2x^2+x>=15 }}} Thank you in advance!

Question 209340: I need assistance solving these inequalities. Thank you!
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Thank you in advance!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I need assistance solving these inequalities. Thank you!
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(x/5)-6<=-(x/2)+6
Multiply both sides by 10 to get:
2x - 60 <= -5x + 60
7x <= 120
x <= 120/7
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x^2-x-6 < 0
(x-3)(x+2) < 0
Draw a number line and mark x=-2 and x = 3 on it.
Check for answers to the inequality in the resulting three intervals.
Test x = -5 in the inequality: (-)(-) < 0 ; false
Test x = 0 in the inequality: (-)(+) < 0 ; true so solutions in (-2,3)
Test x = 10 in the inequality: (+)(+) < 0 ; false
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Solution: (-2,3) or -2 < x < 3
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2x^2+x >= 15
2x^2 + x - 15 > = 0
(x+3)(2x-5) > 0
Draw a number line and mark x = -3 and x = 5/2
Test x = -10 in the inequality: (-)(-) >=0 true so solutions in (-inf,-3]
Test x = 0 in the inequality: (+)(-) >= 0 false
Test x = 10 in the inequality:(+)(+)>= 0 true so solutions in [5/2,+inf)
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Solution: (-inf,-3)U(5/2,+inf)
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Cheers,
Stan H.
Reply to stanbon@comcast.net

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