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Warmups
10 23
x 2( 4) 3( 1)x x
Translate: The product of 7 and m is at most 10
Solve and graph each inequality:
7 2 1 19x
7-4 Compound Inequalities
Objective: To solve and graph “or” inequalities
Compound Inequality
More than one “and” “or”
today
Example 1: x > 2 or x < -4
Graph on the same number line:
These answers These answersor
Example 2
Graph x < 2 or x > 6
TOO
1. x < -3 or x > 4
2. x > 5 or x < 0
3. x > -5 or x < -7
Write your own…
Write a compound inequality for each solution set shown below:
3.
4.
-2 30
0 5
What about…
5. x < 4 or x > -3
6. x > 3 or 4 < x
7. x – 2 < 0 or 2x + 4 > 8
“All numbers”
TOO – Solve and graph
8. 4x – 5 > 7 or 4x – 5 < -9
9. -1 + x < 3 or –x < -4
10. 3n + 11 < 13 or 2n > 5n - 12
x > 3 or x < -1
All numbers
n < 4
AND vs. OR
AND OR
“and” or no word Must say “or”
Both true One or more true
Special case: No solution Special case: All numbers
Homework
Pg. 410 # 26, 27, 28, 31, 33, 37, 38, 40, 41, 42
Math Lab
Inequalities Review
Tic Tac Toe
AND vs. OR
AND OR
“and” or no word Must say “or”
Both true One or more true
Special case: No solution Special case: All numbers
Translate
•The difference of x and 3 is more than 7.
•The product of 3 and y is at least 10.
•A number decreased by 5 is at least 13.
•Twice a number is less than or equal to the number increased by 3
•A number decreased by 8 is at most 1.
Solve and graph
No solution
2 5 2x
Solve and graph
or3 2 5a 7 3 2( 3)a a
-1 10
1; ; 1a or a
Solve and graph
and
x<1
2 4 6x 2 4x x
1
Solve and graph
y > -1 and y < 3
3 2 3y y y
-1 3
Solve and graph
or
All numbers
2 5 7a 2 3a a
Solve and graph
Write a compound inequality for each solution set shown below:
3.-3 60
3; ; 6x or x
Solve and graph
Write a compound inequality for each solution set shown below:
0 5
0 5x
Solve each inequality.
220
5x 50x
10 10x 0x
9 x 9x
Solve each inequality.
6 24
x 16x
3( 2) 4( 3)x x 18x
336
4x 48x
Solve each inequality.
1 4x 5x
2 16
x 18x
3( 3) 4( 2)x x 17x
Determine Value of r.
5(4, )( , 2)
3r r m
7r
3(3, )( ,5)
5r r m
8r