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Objectives, continued: ~

6) Solve inequalities using "and" 7) Solve double inequalities [same as "and", but different notation] 8) Solve inequalities using "or"

Examples Solve the compound inequality. a) Graph the solution. b) Write the solution set notation. c) Write the solution in interval notation.

1) 2x-5 > -1 and 4x+ 2s;16

2) -3x+4>-5 and .!.x+7s;5 2

3 3)

2x-2>1 and-(x+2)~2

4) 0s;-2x+6s;14

5) _!_x-3 1 2

1 6) 2 - 3x ~ 5 or - - x + 1 > -2

2

7) In 2012, a married couple filing jointly who were in the 25% tax bracket paid between $9735 and $27735 in federal income taxes. Federal income tax for this category is $9735 plus 25% of taxable income over $70, 700. Find the range of taxable incomes into which a couple must fall to have been in the 25% tax bracket.

Math 45 2.8-lst: Writing Intervals using Interval Notation & Inequality Notation & Graphing Intervals

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Writing in Interval Notation Interval notation is an abbreviation for the shaded part of the graph. You must have a mental image of the

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Interval notation has four parts, in this order: Left punctuation - left endpoint - right endpoint - right punctuation The left endpoint must be smaller than the right endpoint. When the endpoint is - 00 or 00 , we use parentheses.

Example: -1 < x ::::; 3 is (-1,3] in interval notation. (See graph 6)

Write in interval notation:

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