How do I write the solution set of {x| } for
Find all the critical values by setting each of the factors on the
left = 0
x + 20 = 0 gives critical value x = -20
x - 10 = 0 gives critical value x = 10
x + 11 = 0 gives critical value x = -11
Mark them on a number line:
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-22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
Choose a value left of -20, the left-most critical value,
say x = -21. Test it by substituting in the inequality:
That is false so we DO NOT shade the part of the number line
left of -20. So we still have the unshaded number line
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-22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
Choose a value between -20 and -11, say x = -12. Test it by substituting in the inequality:
That is true so we DO shade the part of the number line between -20 and
-11. So we have:
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-22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
Choose a value between -11 and 10, say x = 0. Test it by substituting in the inequality:
That is false so we DO NOT shade the part of the number line between -20 and
-11. So we still have:
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-22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
Choose a value right of 10, the right-most critical value,
say x = 11. Test it by substituting in the inequality:
That is true so we DO shade the part of the number line to the right of
10. So we have:
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-22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
In set-builder notation the solution set is written:
{x | -20 < x < -11 OR x > 10}
In interval notation the solution set is written:
(-20,-11) U (10,)
Edwin