Module 9 : Absolute Value Equations and Inequalities
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| If A={x/x is an even number greater than 0 and less than 10} and B={3,4,5,6}, find A n B. | n=intersection
List A={2,4,6,8} 4 and 6 are in both sets A and B therefore the answer is {4,6}
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| If A={x/x is an even number greater than 0 and less than 10} and B={3,4,5,6} find A U B. | U=Union
A={2,4,6,8}
B={3,4,5,6}
A U B={2,3,4,5,6,8}
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| Solve 2<4-x<7 | 2 < 4-x < 7
2-4 < 4-x-4 <7-4 Subtract 4 from each side
-2 > -x > 3 symbols will reverse because the numbers are now negative
Divide all sides by -1
2 > x > -3
Solution = (-3,2)
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| Solve IxI=4 | IxI = 4 IxI = 4
I4I = 4 I-4I = 4
4 = 4 True 4 = 4 True
Solution {-4,4}
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| Solve I2xI + 5 = 7 | I2xI + 5 = 7
I2xI = 2 Subtract 5 from both sides
2x = 2 or 2x = -2 Divide by 2
x = 1 or x = -1
{-1,1}
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| Solve I2x+5I = -1 | No solution
An absolute value of an expression is never negative
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| Solve Ix-3I = I5-xI | x - 3 = 5 - x or x - 3 = - ( 5 - x )
2x - 3 = 5 Add x x - 3 = - 5 + x Rewrite
2x = 8 Add 3 -3 = -5 False
x = 4
Solution {4}
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| Solve for x Ix-6I < 2 | -2 < x-6 < 2
-2 + 6 < x-6+6 < 2 + 6 Add 6
4 < x < 8
(4,8) solution
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Created by:
skommer
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