•To be able to solve and graph compound inequalities.
Today’s Objective
• Here is a list of all the different inequality signs.
Review
•<, >, <, >
Compound Inequalities •Compound Inequalities are inequalities that involve the use of the AND and OR conjunctions.
For Instance
Compound Inequalities •Here is an example of an AND problem. •Is it true that today it is raining and it is Wednesday?
Compound Inequalities •Here is an example of an OR problem. •Is it true that today it is raining or it is Wednesday?
•Now answer the following 2 AND problems.
Compound Inequalities
• 1.) What group can be described as less than seniors, and greater than freshman? • Sophomores and Juniors
Compound Values
•2.) What grade(s) is/are greater than a “D”,and less than a “B” ?
Compound Values
•“C”
•Now answer the following 2 OR problems.
Compound Inequalities
• 1.) What group can be described as less than Sophmores, or greater than Juniors? • Freshmen or Seniors
Compound Values
•2.) What grade(s) is/are greater than a “B”,or less than a “D” ?
Compound Values
•“A” or “F”
• Consider the following information. • Assume that X represents a true value like Today is Wednesday and then consider that Y represents a true Value like it is January.
Compound Values
• Then is it True If we say: • X and Y In other words is it true that It is Wednesday and January?
Compound Values
• Now is also true if we use the OR conjunction • X or Y • In other words is it true if we say it is Wednesday or January ?
Compound Values
• Lets make a table of these values.
Truth Table
• Now, make up other true and false values for X and Y and check them yourselves. Like X represents it is Wednesday and Y represents it is July. • In other words check for X is true and Y is False, then check
Compound Values
• X is false and Y is true, and finally check for when they are both false. • Then fill in the table with the correct true and false values.
Compound Values
Compound Inequalities •Next is an example of writing and graphing an AND Inequality and then an example of writing and graphing an OR Inequality.
Compound Inequalities
• 1.) All real numbers that are greater than or equal to zero and less than 4.
•0 < x < 4
Compound Inequalities •2.) All real numbers that are less than -1 or greater than 2.
•x < -1
or
x > 2
Compound Inequalities •Now for some math examples. Read the following two examples, one of them is an AND and the other is an OR.
•-2 < 3x - 8 < 10
1.) Solve a compound inequality (And)
•Step 1: Isolate the variable between the two inequality signs.
•-2 < 3x - 8 < 10(add 8) •-2+8 <3x-8+8< 10+8 •6 < 3x < 18(divide by 3) • 6/3 < 3x/3 < 18/3 • 27
•Step 1: Solve each part separately.
2.) Solve a compound inequality (Or)
3x + 1 < 4 2x - 5 > 7 3x+1-1 < 4-1 2x-5+5 > 7+5 2x > 12 3x < 3 2x/2 > 12/2 3x/3 < 3/3 x>6 x<1
Solve a compound inequality
•-2 < -2 - x < 1
3.) Solve a compound inequality (AND)
• Step 1: Isolate the variable between the two inequality signs.
• -2 < -2 - x < 1(add 2)
Isolate the variable
• -2+2 <-2+2-x < 1+2 • 0 < -x < 3(divide by -1) • 0/-1 < -x/-1 < 3/-1 • 0 > x > -3
Both signs reverse direction