Download Notes Solving Inequality statements

March 6, 2017
Warm-Up -Determine which of the given numbers are solutions to
the inequality. Show work!
1.
y > 4;
2, 3, 4, 5, 6
2.
2x + 3 > 8 ;
3.
3m - 11 ≤ 2m - 4;
1, 2, 3, 4, 5
5, 6, 7, 8
Name all numbers that all solutions to:
4. p < 7
OBJ: Solve Inequalities and Review
Graphing
Ex 1 Consider the inequality x < 9
Say it in words.
Graph it.
-10
-9
-8
-7
-6
-5 -4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
Name a point in the solution set.
Check that it works.
Always check a point that is
NOT an endpoint!
March 6, 2017
IMPORTANT! USE AN OPEN OR CLOSED CIRCLE FOR GRAPHS OF INEQUALITIES
Open Circle -Closed Circle --
Ex 2 Graph the solutions to m ≥ 4
-10
-9
-8
-7
-6
-5 -4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
March 6, 2017
Ex 3 Graph the solutions to 5 < y
-10
-9
-8
-7
-6
-5 -4
-2
-3
-1
0
1
2
3
4
5
6
7
8
10
9
IMPORTANT! SOMETIMES YOU SHOULD REWRITE THE INEQUALITY SO
THE VARIABLE IS ON THE LEFT SIDE.
CHANGE THE DIRECTION OF THE INEQUALITY.
Practice Problems - Graph the solutions
PP1
-10
-9
x>5
-8
PP2
-10
-9
-9
-8
-9
-5 -4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
-7
-6
-5 -4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
m ≥ -4
-8
PP4
-10
-6
y≤7
PP3
-10
-7
-7
-6
-5 -4
2>k
-8
-7
-6
-5 -4
March 6, 2017
Ex 4 Solve and Graph the solutions to 2x +1 < 9
-10
-9
-8
-7
-6
-5 -4
-2
-3
-1
0
1
2
3
4
5
6
7
8
10
9
IMPORTANT! CHECK IN THE ORIGINAL INEQUALITY
Practice Problems - Solve, Graph and Check the solutions
PP5
x+4>7
-10
-9
-8
-7
-6
-5 -4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
-9
-8
-7
-6
-5 -4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
PP6 2m + 5 ≥ -11
-10
March 6, 2017
Solve and graph
the inequality
and show a
check.
1. 3x + 1 > -11
2. 2m + 5 ≥ 7