Do Now 12/18/09Do Now 12/18/09

Copy HW in your planner.Copy HW in your planner. Text p. 384, #5-10 all, 18-30 even, 38 & 40Text p. 384, #5-10 all, 18-30 even, 38 & 40 Quiz sections 6.1 - 6.4 TuesdayQuiz sections 6.1 - 6.4 Tuesday

In your notebook, put the following heading In your notebook, put the following heading on a new page in your notebook. on a new page in your notebook.

““Section 6.4, Solve Compound Section 6.4, Solve Compound Inequalities.”Inequalities.” Then list five examples of Then list five examples of compound words. compound words.

COMPOUND INEQUALITYCOMPOUND INEQUALITY – – consists of two separate inequalities consists of two separate inequalities joined by joined by ANDAND or or OROR..

Section 6.4Section 6.4“Solve Compound Inequalities”“Solve Compound Inequalities”

““AND” AND” Compound InequalitiesCompound Inequalities

The graph of a compound inequality with The graph of a compound inequality with ANDAND is the is the INTERSECTIONINTERSECTION of the graphs of the inequalities. of the graphs of the inequalities.

Graph x > -2Graph x > -2

00 11-1-1 22-2-2 33

Graph x ≤ 1Graph x ≤ 1

00 11-1-1 22-2-2 33

Graph of x ≤ 1 and x > -2Graph of x ≤ 1 and x > -2

00 11-1-1 22-2-2 33

““OR” OR” Compound InequalitiesCompound Inequalities

The graph of a compound inequality with The graph of a compound inequality with OROR is the is the UNION UNION of the graphs of the inequalities.of the graphs of the inequalities.

Graph x > 2Graph x > 2

00 11-1-1 22-2-2 33

Graph x ≤ -1Graph x ≤ -1

00 11-1-1 22-2-2 33

Graph of x ≤ -1 or x > 2Graph of x ≤ -1 or x > 2

00 11-1-1 22-2-2 33

Translate the verbal phrase into an inequality. Then Translate the verbal phrase into an inequality. Then graph the inequality.graph the inequality.

All real numbers that are greater than All real numbers that are greater than –– 22 and and lesslessthan than 3.3.

InequalityInequality::

Graph:Graph:

All real numbers that are less than All real numbers that are less than 00 or or greater thangreater thanor equal to or equal to 2.2.

Inequality:Inequality:

Graph:Graph:

– – 2 < 2 < x x < 3< 3

x x < 0 < 0 or x or x ≥ 2≥ 2

SolveSolve

Solve a Compound Inequality with ANDSolve a Compound Inequality with AND

2 < 2 < x x + 5 < 9.+ 5 < 9. Graph your solutionGraph your solution..

Separate the compound inequality into two Separate the compound inequality into two inequalities. Then solve each inequality separately.inequalities. Then solve each inequality separately.

2 < 2 < x x + 5+ 5 Write two inequalities.Write two inequalities.

2 2 – 5– 5 < < x x ++ 5 5 – 5– 5 Subtract Subtract 55 from each side. from each side.

-3 < -3 < xx Simplify.Simplify.

The compound inequality can be written as The compound inequality can be written as – 3 < – 3 < x x < 4.< 4.

x x + 5 < 9+ 5 < 9

x x ++ 5 5 – 5– 5 < 9 < 9 – – 55

x x < 4< 4

andand

andand

andand

SolveSolve

Solve a Compound Inequality with ANDSolve a Compound Inequality with AND

––7 < 7 < x x – 5 < -1– 5 < -1.. Graph your solutionGraph your solution..

Separate the compound inequality into two Separate the compound inequality into two inequalities. Then solve each inequality separately.inequalities. Then solve each inequality separately.

––7 < 7 < x x – 5– 5 Write two inequalities.Write two inequalities.

––77 + 5+ 5 < < x x –5–5 + 5+ 5 Add Add 55 to each side. to each side.

––2 < 2 < xx Simplify.Simplify.

The compound inequality can be written as The compound inequality can be written as – 2 < – 2 < x x < 4.< 4.

andand x x – 5 < -1– 5 < -1

x x –– 5 5 + 5+ 5 < -1 < -1 + 5+ 5

x x < 4< 4

andand

andand

– – 3 – 2 – 1 0 1 2 3 4 5 3 – 2 – 1 0 1 2 3 4 5 Graph:Graph:

Write original Write original inequality.inequality.

Solve Solve 22x x + 3 < 9 + 3 < 9 oror 33x x – 6 > 12.– 6 > 12. Graph your solution. Graph your solution.

Solve the two inequalities separately.Solve the two inequalities separately.

22x x + 3 < 9+ 3 < 9 oror 33x x – 6 > 12– 6 > 12

22x x ++ 3 3 – 3– 3 < 9 < 9 – 3– 3 oror 33x x –– 6 6 + 6+ 6 > 12 > 12 + 6+ 6 Addition or Subtraction Addition or Subtraction property of inequalityproperty of inequality

22x x < 6< 6 oror 33x x > 18> 18 Simplify.Simplify.

Solve a Compound Inequality with ORSolve a Compound Inequality with OR

x x < 3< 3 oror x x > 6> 6 Simplify.Simplify.

The solutions are all real numbers less than The solutions are all real numbers less than 33 or or greatergreater than than 66..

Solve Solve Graph your solution.Graph your solution.

Solve the two inequalities separately.Solve the two inequalities separately.

Solve a Compound Inequality with ORSolve a Compound Inequality with OR

33hh + 1< – 5 + 1< – 5 oror 22hh – 5 > 7 – 5 > 7

Simplify.Simplify.

33hh + 1< – 5 + 1< – 5 Write two inequalitiesWrite two inequalities..

Addition & Addition & Subtraction propertySubtraction propertyinequalitiesinequalities..

33hh < – 6 < – 6

oror 22hh – 5 > 7 – 5 > 7

33hh + 1 + 1 – 1– 1< – 5 < – 5 – 1– 1 oror 22hh – 5 – 5 + 5+ 5 > 7 > 7 + 5+ 5

oror 22hh > 12 > 12

hh < – 2 < – 2 oror hh > 6 > 6

––7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 77 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7

What Did You Learn Today?What Did You Learn Today?

““OR” statementOR” statement

““AND” statementAND” statement

HomeworkHomework Text p. 384, #5-10 all, 18-30 even, 38 & 40Text p. 384, #5-10 all, 18-30 even, 38 & 40

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Make a TRAIN…Make a TRAIN…

Player #1 selects a block.Player #1 selects a block. Player #2 selects a block that has only Player #2 selects a block that has only

ONE attribute that is DIFFERENT and ONE attribute that is DIFFERENT and places it next to the first. places it next to the first.

Players #3 & #4 repeat this pattern.Players #3 & #4 repeat this pattern.

Which group can make the longest train Which group can make the longest train the fastest?the fastest?