View
225
Download
0
Category
Preview:
Citation preview
8/3/2019 Compound Inequalities Alg2H
1/17
Click to edit Master subtitle style
Compound Inequalities
Logic Operators: OR & ANDInterval Notation
8/3/2019 Compound Inequalities Alg2H
2/17
There are two different notations, when you writeyour answers you can use inequality notation or
interval notation.
0 4 6 82-7-6-5-4-3-2 -1 1 5 73 2-7-6-5-4-3-2 -1 1 5 730 4 6 8[
1x
Inequality notationfor graphs shownabove.
[ 1, )x
Interval notationfor graphs shownabove.
8/3/2019 Compound Inequalities Alg2H
3/17
),1[
Let's have a look at the interval notation.
For interval notation you list the smallestx
canbe, a comma, and then the largestxcan be sosolutions are anything that falls between thesmallest and largest.
This means x is
unboundedabove
2-7-6-5-4-3-2 -1 1 5 730 4 6 8[
unbounded
The bracket before the 1 is square because this is greater than "or equal to" (solutioncan equal the endpoint).
The bracket after the infinity sign is rounded because the interval goes on forever(unbounded) and since infinity is not a number, it doesn't equal the endpoint (there isno endpoint).
8/3/2019 Compound Inequalities Alg2H
4/17
]4,2(
Let's try another one.
2-7-6-5-4-3-2 -1 1 5 730 4 6 8
Rounded bracket means
cannot equal -2
Squared bracket meanscan equal 4
The brackets used in the interval notation above are the same onesused when you graph this.
( ]
This means everything between 2 and 4 but not including -2
8/3/2019 Compound Inequalities Alg2H
5/17
2-7-6-5-4-3-2 -1 1 5 730 4 6 8
)4,(
Let's look at another one
This means x isunbounded
below
Notice how the bracket notation for graphing corresponds to the brackets ininterval notation.
Remember that square is "or equal to" and round is up to but not equal. Bythe infinity sign it will always be round because it can't equal infinity (that is
not a number).
This means the
largest x can be is 4but can't equal 4
)
8/3/2019 Compound Inequalities Alg2H
6/17
OR" compound inequality
3or2 < xx
There are two intervals to list when you list in
interval notation.
2-7-6-5-4-3-2 -1 1 5 730 4 6 8) [
)2,( ),3[
When the solution consists of more than one interval,we join them with a union sign.
8/3/2019 Compound Inequalities Alg2H
7/17
EXAMPLE Solve an or compound inequality
Solve 3x+ 5 11 or 5x 7 23 . Then graph the solution.
SOLUTION
A solution of this compound inequality is a solution ofeitherof its parts.
First Inequality Second Inequality
3x + 5 11
3x 6
x 2
Write firstinequality.
Subtract 5 from eachside.Divide each side by3.
5x 7 23
5x 30
x 6
Write secondinequality.
Add 7 to eachside.Divide each side by5.
8/3/2019 Compound Inequalities Alg2H
8/17
EXAMPLE Solve an or compound inequality
ANSWER
The graph is shown below. The solutions are all realnumbers less than or equal to 2orgreater than or equalto 6.
8/3/2019 Compound Inequalities Alg2H
9/17
EXAMPLE Solve an and compound inequality
Solve 4 < 6x 10
14.
Then graph the solution.
4 < 6x 10 14
4 + 10< 6x 10 + 10 14 + 10
6 < 6x 24
1
8/3/2019 Compound Inequalities Alg2H
10/17
EXAMPLE Write and use a compound inequality
Biology
A monitor lizard has atemperature thatranges from 18Cto34C. Write the rangeof temperatures as acompound inequality.Then write aninequality giving thetemperature range in
degrees Fahrenheit.
8/3/2019 Compound Inequalities Alg2H
11/17
EXAMPLE Write and use a compound inequality
SOLUTION
The range of temperatures Ccan be represented by the inequality 18 C34. LetFrepresent the temperature in degrees Fahrenheit.
18 C 34 Writeinequality.
18 3459
(F 32)
32.4 F 32 61.2
64.4 F 93.2
Substitute forC.9
5(F 32)
Multiply each expression by ,
the reciprocal of .
9
55
9
Add 32 to eachexpression.
8/3/2019 Compound Inequalities Alg2H
12/17
EXAMPLE Write and use a compound inequality
ANSWER
The temperature of the monitor lizard ranges from64.4Fto 93.2F.
8/3/2019 Compound Inequalities Alg2H
13/17
PRACTICE
Solve the inequality. Then graph the solution.
9. 1 < 2x + 7 < 19
ANSWER
The solutions are all real numbers greater than 4and less than 6.
4
8/3/2019 Compound Inequalities Alg2H
14/17
PRACTICE
Solve the inequality. Then graph the solution.
10.8 x 5 6
The solutions are all real numbers greater than andequal to 11 and less than and equal to 3.
ANSWER
11 x 3
8/3/2019 Compound Inequalities Alg2H
15/17
PRACTICE
Solve the inequality. Then graph the solution.
11.x + 4 9 orx 3 7
ANSWER
The graph is shown below. The solutions are all realnumbers.
less than or equal to 5orgreater than or equal to 10.
x 5 orx10
8/3/2019 Compound Inequalities Alg2H
16/17
PRACTICE
Solve the inequality. Then graph the solution.
12. 3x 1< 1 or2x + 5 11
x < 0 orx3
less than 0orgreater than or equal to 3.
ANSWER
The graph is shown below. The solutions are all realnumbers.
8/3/2019 Compound Inequalities Alg2H
17/17
PRACTICE
1
3.
WHAT IF? In Biology example, write a compound
inequality for a lizard whose temperature ranges from15Cto 30C. Then write an inequality giving thetemperature range in degrees Fahrenheit.
15 C 30 or59 F 86
ANSWER
Recommended