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Lesson23 - Lessons 23 Sections 4.2 and 4.3 3-part...

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1 Lessons 23 Sections 4.2 and 4.3 3-part Inequality, Absolute Value Inequalities 3-Part Inequality: 2 10 10 AND 2 x x x < < < > The number must meet both conditions, therefore the conjunction ‘and’. Where are these numbers on the number line? These numbers are between 2 and 10. This can be written as 2 10 x < < , a 3-part inequality. Solve the following: 1) 12 4 3 12 + < - x 2) 10 3 2 0 x > - > Examine this statement: 3 2 x or x < - > With an ‘or’ statement, only the first condition or only the second condition must be true. Where are these numbers on the number line? These are the numbers found in two ‘rays’ in opposite directions. Many students try to write this as a 3-part inequality: 3 2 x - > > . However, this implies 3 2 - > , which is false. This type of situation is not a 3-part inequality. Examine: 2 < x Solutions include 87 . 1 , 999 . 1 , 8 7 1 , 2 3 , 1 , 0 - - - These are the numbers that are less than 2 units from zero. Examine where these are on a number line: -2 2 2 2 x - < < 0 2 4 6 10 8 -2 -4 -6 -8 -10 0 2 4 6 10 8 -2 -4 -6 -8 -10 ( )
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2 Examine: 2 > x Solutions include
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