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

Chapter 2 Section 6

Inequalities


Assignment 11

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

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

Solutions to Inequalities

  • Determine if the following are solutions to the given inequality


Ordering numbers

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

From The Text


Some notation

Some Notation

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


Set builder

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 builder1

Set-Builder

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


Solutions to inequalities1

Solutions to Inequalities

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


Shade each on a number line

Shade each on a number line.


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

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


Let a b and c be any numbers

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

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

Examples


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

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


Examples1

Examples


Solving inequalities

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 turn give solution in set builder interval and number line

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


Your turn give solution in set builder interval and number line1

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


Your turn give solution in set builder interval and number line2

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


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