Download ®Interval notation: used to represent solution sets ®______ interval

€ Linear
inequality: Ax + B < C
of an inequality- any number that
makes the inequality _______.
€ Signs
g
€ < Less than
< Less than or equal
€ > Greater than > Greater than or equal
€ _______: a number line indicating
solutions of any inequality.
€ Solution
Objective: To graph intervals
and solve inequalities.
€Interval
notation: used to represent
solution sets
€_______ interval: use parenthesis
( ); use with < or >; does _______
include endpoint
€closed interval: use brackets [
];
use with < or > ; _______ endpoint
€Note: An interval can be half-open.
€ Closed
interval [a,b] represents the set of real
numbers between and including a and b.
€ Open
interval (a,b) represents the set of real
numbers between but not including a and b.
Example: (a,b) = {x | a < x < b }
Graph:
x is ggreater than a
( a< x) and x is less
than b (x < b) or
“x is between a
and b, exclusive”
Infinite intervals
€ _______
represents the set of real numbers
greater than a;
{x | x > a}
Example: [a,b] = {x a < x < b }
Graph:
x is greater than or
equal to a ( a < x)
and x is less than or
equal to b (x < b) or
“x is between a and
b, inclusive”
€ _______
represents the set of real numbers less
than or equal to b; {x | x < b}
€ _______
represents all real numbers.
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€ Express
each interval in set-builder notation and
graph.
A) [-2,5)
B) [1, 3.5]
C) (-∞,-1)
€ Write in interval notation and graph.
D) x < 5
E) x > -3
F) -4 < x < 2
are the same as with
equations…
Use the GOLDEN RULE.
RULE
G) p + 6 < 8
H) 8x < 7x - 6
€Note:
Always write an
inequality with the _______
on the left.
I) Solve, check, and graph the
solution set of 2k – 5 > 1 + k.
Get _______ on one side by itself by
performing the inverse operation.
EXCEPTION: If you multiply or divide
by a _______ number,
number you must
REVERSE the inequality symbol.
2. Graph the solution on a number
line.
3. Verify _______ your solution.
1.
2
Multiply both sides of each inequality by -5.
J) 7 < 8
K) -1 > -4
L) 2x < -10
M) -7k > 8
N) -9m < -81
1
3
(m + 3) + 2 ≤ (m + 8)
4
4
O) 5 – 3(m – 1) < 2(m + 3) + 1
P)
Q) -3 < x – 1 < 7
R) 5 < 3x – 4 < 9
3
€A
solution of an inequality is any number that
makes the inequality true.
€ Graphs
of inequalities indicate all possible
solutions. Use interval notation and symbols.
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