Question 99397
solve  the  inequality {{{ (x+2)(x-1)(x-3)<or=0}}}
Write the answer in set notation and interval notation.
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Solve the EQUALITY:
x = -2, x=1, x=3
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Draw a number line.
Mark x=-2, x=1, and x=3 on the line.
They divide the line into four intervals.
Look for solutions for the INEQUALITY in each of the intervals.
Do this by inserting a test value into (x+2)(x-1)(x-3)<0:
In (-inf,-2)select x=-3; you get -*-*- <0 so there are solutions here
In (-2,1) select x=0; you get +*-*->0 so no solutions here
In (1,3) select x=2; you get +*+*-<0 so solutions here
In (3,+inf) select x=4; you get +*+*+>0 so no solutions here
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Final answer:
Interval notation: [-2,1] or [1,3]
Set notation: {x|-2<=x<=1}U{x|1<=x<=}
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Cheers,
Stan H.