Question 249832: Solve the following inequalities algebraically.
1. 2x^2≥-8x-4
2. 2x^2>5x
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Solve the following inequalities algebraically.
1. 2x^2≥-8x-4
1st: Solve the EQUALITY:
2x^2 = 8x-4
x^2 = 4x-2
x^2-4x+2 = 0
x = [4 +- sqrt(16-4*2)]/2
x = [4 +- sqrt(8)]/2
x = 2 + sqrt(2) = 3.414.. or x = 2 - sqrt(2) = 2-1.414..= 0.586..
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2nd: Draw a number line and plot x = 0.586 and x = 3.414
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3rd: Solve the INEQUALITY by testing values for each of the
number line intervals in x^2-4x+2 > 0
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Check x = 0 to get: 0 + 0 + 2 > 0 ; true, so solutions in (-inf,2-sqrt(2))
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Check x = 1 to get: 1-4+2 > 0 ; false, so no solutions in (2-sqrt(2),2+sqrt(2))
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Check x = 4 to get: 16 - 16 + 2 > 0 ; true, so solutions in (2+sqrt(2),+inf)
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Final Answer: (-inf,2-sqrt(2))U(2+sqrt(2),+inf)
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Cheers,
Stan H.
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I'll leave the 2nd problem to you.
2. 2x^2>5x
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