Download Interval Notation and Review of Inequalities

Algebra II Notes
Name: _______________________ Date: ________
First Degree Inequalities and Interval Notation
Interval Notation is another way for denoting the solution for an inequality by describing the interval
containing the numbers that satisfy that inequality.
The numbers at the end of the interval are enclosed in brackets [ or ] (the boundary is a solution/ filled in circle) or
parentheses ( or ) (the boundary point is not a solution/open circle).
If an interval extends forever to the right then the right endpoint is heading towards positive infinity or 
If an interval extends forever to the left then the left endpoint is heading towards negative infinity or 
Read the graph (number line) _____________to ____________to help write the solution.
When graphing on a number line, an_________________ circle indicates that it is not a solution but is a boundary and a
______________________ circle indicates that it is a solution as well as a boundary.
Examples and Practice: Complete all missing pieces of the chart.
Inequality
Words
Graph
A) x  3
x is less than 3
Interval
Notation
(,3)
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
B) x  3
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
C) x  3
D)
x is less than or equal to
3
x is greater than or equal
to 3
(,3]
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
E) a  2
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
F) m 
5
2
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
G)
H)
(, 1]
c is greater than 6
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
I)
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
J)
K)
b is less than or equal to 0
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
3
( , )
2
Solving linear ineqalities.
Inequality
L)
Words
Complete all missing pieces of the chart.
Graph
2x  5  3
Interval
Notation
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
M)
x
2
5
N)
3
x  6  ( x  1)
4
O)
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
b  2
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
***Remember to switch the direction of your inequality when you multiply or
divide both sides of the inequality by a negative!
Solving Pairs of Inequalities.
Inequality
Complete all missing pieces of the chart.
Words
Graph
Interval
Notation
P) a  1 and a  5
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
Q) 9  b  0
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
R)
S)
t is less than 4
or is greater
than 6
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
( 5,3]
T)
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
U)
V) 3x 1  2
and
2(5  x)  16
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
W) 3(2 x  4)  1  7 or 7 x  7
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
X) 14  5( x  3)  1  11
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
Y) b  0 or b  2
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11
Z) b  0 and b  2
-10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11