Download 7-4 Compound Inequalities

Warmups
Translate: The product of 7 and m is at most 10
Solve and graph each inequality:
x
 10  2
3
2( x  4)  3( x  1)
7  2x 1  19
7-4 Compound
Inequalities
Objective: To solve and graph
“or” inequalities
Compound Inequality

More than one

“and” “or”
Example 1:
today
x > 2 or x < -4
These answers
or
These answers
Graph on the same number line:
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.
-2
0
3
4.
0
5
What about…
5. x < 4 or x > -3
“All numbers”
6.
x > 3 or 4 < x
7.
x – 2 < 0 or 2x + 4 > 8
TOO – Solve and graph
8.
4x – 5 > 7 or 4x – 5 < -9
x > 3 or x < -1
9.
-1 + x < 3 or –x < -4
All numbers
10.
3n + 11 < 13 or 2n > 5n - 12
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
2  x  5  2
No solution
Solve and graph
3a  2  5
or
7  3a  2(a  3)
a  1; or ; a  1
-1
0
1
Solve and graph
2x  4  6
and
x<1
1
x  2x  4
Solve and graph
3  y  2 y  3  y
y > -1 and y < 3
-1
3
Solve and graph
2a  5  7
All numbers
or
2a  a  3
Solve and graph
Write a compound inequality for each solution
set shown below:
3.
-3
0
6
x  3; or ; x  6
Solve and graph
Write a compound inequality for each solution
set shown below:
0 x5
0
5
Solve each inequality.
2
x  20
5
x  50
x 10  10
x0
9  x
x  9
Solve each inequality.
x
6 2
4
x  16
3( x  2)  4( x  3)
x  18
3
x  36
4
x  48
Solve each inequality.
1  x  4
x  5
x
 2 1
6
x  18
3( x  3)  4( x  2)
x  17
Determine Value of r.
5
(4, r )(r , 2)m 
r 7
3
3
(3, r )(r ,5) m 
5
r 8