Chapter 2 section 6
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Chapter 2 Section 6. Inequalities. Assignment 11. Work the review Parts 1 and 2 for the Opportunity, PDF version in Resources.

Work Section 2.6: P. 147: 6, 7, 9, 12, 15, 20, 22, 23, 26, 27, 40, 41, 45-48, 66-68, 75- 80. Activity #4, Cash Register Receipt.

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Chapter 2 Section 6

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Chapter 2 Section 6

Inequalities


Assignment 11

  • Work the review Parts 1 and 2 for the Opportunity, PDF version in Resources.

Work Section 2.6: P. 147: 6, 7, 9, 12, 15, 20, 22, 23, 26, 27, 40, 41, 45-48, 66-68, 75-80


Activity #4, Cash Register Receipt

  • Do not show the receipt to your partner.

  • Tell them what the total was and the tax rate. Ask them to tell you the pretax total (the subtotal).

  • Once they have given you the value, show them the receipt and see if it matches. If not, call me over and let’s see where the confusion lies.


Solutions to Inequalities

  • Determine if the following are solutions to the given inequality


Ordering Numbers

  • a > b if a lies to the right of b on the number line.

  • a < b if a lies to the left of b on the number line.


From The Text


Some Notation

  • Two ways to describe solution sets to inequalities are set-buildernotation and interval notation.


Set-Builder

  • Example (a) is read “x such that x is an element of the real numbers

  • Example (b) is read “y such that y is greater than 3”


Set-Builder

  • In general you read it as “ the set of values such that they meet the specified condition”


Solutions to Inequalities

  • Write the solution to the given inequalities as a number line graph.


Shade each on a number line.


Use set-builder and interval notation to describe the given number line


Let a,b, and c be any numbers.

  • Addition Property of Inequality

  • if a > b, then a + c > b + c

  • Subtraction Property of Equality if a > b, then a - c > b - c


Let a,b, and c be any numbers, where c is positive.

  • Multiplication Property of Inequalityif a > b, then a(c) > b(c)

  • Division Property of Equalityif a > b, then a / c > b / c


Examples


Let a,b, and c be any numbers, where c is negative.

  • Multiplication Property of Inequalityif a > b, then a(c) < b(c)

  • Division Property of Equalityif a > b, then a / c < b / c


Examples


Solving Inequalities

  • To solve an inequality, do the following:

  • Simplify each side of the inequality.

  • Isolate the variable by addition or subtraction.

  • Solve the inequality by multiplication or division.

  • Use a graph, interval motation or set builder notation to describe the solution.


Your TurnGive solution in set-builder, interval, and number line


Your TurnGive solution in set-builder, interval, and number line


Your TurnGive solution in set-builder, interval, and number line


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