Today:

Warm Up

Set-Builder Notation

Compound Inequalities

Class Work

November 14, 2014

New @ v6math.blogspot.com

News & Notes

1st Quarter grades will be posted @ v6math. today.

First three topics for Khan Academy due this Sunday.

Reminder: To receive credit for submitted class work, you must show all steps leading to your solution.

Warm-Up Section

of Notebook

Warm-Up: Multi-Step Inequalities

1. 3x -12x + 8 > -2 - 4x;

-5x > -10;

x < 2

x < 4

3. -2x > 19;

2. 4x < 16

2. 6x - 4 < 2x + 12

4.

x < - 19/2; x < - 9 1/2

1. 3x -2(6x - 4) > 4 - (4x + 6)

3. 3x - 15 > 4 + 5x

3. 3x - 15 > 4 + 5x

Multi- Step Inequalities

1. 3x -2(6x - 4) > 4 - (4x + 6)

1. 3x -12x + 8 > -2 - 4x;

-5x > -10; x < 2

2. 6x - 4 < 2x + 122. 4x < 16 x < 4

3. -2x > 19;

x < - 19/2; x < - 9 1/2

4.

of Notebook

“The Set of x such that x is less than or equal to seven”

Solve: x – 9 < -2

x < 7

The solution, in set builder notation, is..

And is read as,

Solving Compound InequalitiesCompound Inequalities are really two

inequalities brought together with the connecting words ‘and’ or ‘or’.

If a compound inequality uses 'and', both inequalities must be true.

The signs should always face the same direction when writing conjunctions without the word and.

Class

Notes

A. Conjunctions: Two inequalities joined by the word ‘and’.

For example: x > -1 and x < 4; This can also be written without the word and by placing the variable between the ‘bookends’ of the smaller and larger values. Try writing the above compound inequality without using and.

-1 < x < 4

B. Disjunction: A compound inequality containing the word ‘or’, is true if one or both inequalities are true.

Compound InequalitiesAll compound inequalities divide the number line

into three separate regions.x

y z

A compound inequality containing the word and is true if and only if (iff), both inequalities are true.

(Conjunctions)

(Disjunctions)

Compound Inequalities A. Conjunction: A compound inequality containing

the word ‘and’ is true if and only if (iff), both inequalities are true.

x5-4 -2 0 2 4-5 -3 1 5-1-5 3

x5-4 -2 0 2 4-5 -3 1 5-1-5 3

x5-4 -2 0 2 4-5 -3 1 5-1-5 3

Example:

1x

2x

2

1

x

and

x

Compound Inequalities

x5-4 -2 0 2 4-5 -3 1 5-1-5 3

x5-4 -2 0 2 4-5 -3 1 5-1-5 3

x5-4 -2 0 2 4-5 -3 1 5-1-5 3

Example:

1x

3x

3

1

x

or

x

B. Disjunction: A compound inequality containing the word ‘or’, is true if one or both inequalities are true.

or

Solving Compound InequalitiesTo solve a compound inequality, you must solve

each part of the inequality separately. Conjunctions are solved when both parts of the inequality are trueOn the same graph, draw the solution to both parts of the conjunction, then write the solution in set builder notation.

x

-1 4

x > -1 and x < 4

{x|-1 < x < 4}

The solution set is the intersection of the two graphs.And is written in set builder notation without

using the word ‘and’ as...

Compound Inequalities

The solution set is therefore: { x| -1 < x < 2}

1. Graph the solution set of x < 2 and x > -1. Write the solution in set builder notation without the word ‘and’.

Compound InequalitiesPractice Problem: Compound Inequality

(Conjunction)2. x < -2 and x – 2 > 1

The Solution is:

No Solution

Write the conjunction without the word ‘and’.Then solve and graph

Compound Inequalities

Practice Problem: Compound Inequality (Disjunction)1. 2x + 1 < 5 or 3x > x + 8

The Solution is: x < 2 or x > 4

x5-4 -2 0 2 4-5 -3 1 5-1-5 3

Class Work:

Class Work 2.1 (Inequalities) should be complete

2.2; Complete today or by start of class Monday

Compound Inequalities

Compound InequalitiesPractice Problem: Compound Inequality

(Conjunction)1. -2 < x – 1< 3

How would we write this

using the word ‘and’?-2 < x - 1 and x –

1< 3x

5-4 -2 0 2 4-5 -3 1 5-1-5 3

The graph of the solution is:

{x|-1 < x < 4}

The written solution is:And is verbalized as:

The set of x such that negative one is less than or equal to x less than four.

|2x – 3| > 6 - x

5. -3(2x - 3) + 7x < -4(x - 5) + 6x – 2

4.

Warm Up

6. Simplify: -6 - (-3) + (-2) * 4 =

7.

9. |x + 5|+ 3 = 11

8. -2|x - 7|- 4 = -22

3. 3x - 15 > 4 + 5x3. -2x > 19;

x < - 19/2; x < - 9 1/2

Warm Up (5)

23 2

3x | 2x + 3 | < 6