Name ________________________________________________________ Date __________Color________
Algebra I
Ms. Hahl
Solving and Graphing Inequalities
Graphing Simple Inequalities:
When finding the solution for an equation we get one answer for x. (There is only one number that satisfies
the equation.) For 3x – 5 = 16, the only solution is x = 7. When we have an inequality to solve (greater than,
less than, greater than or equal to, or less than or equal to) we have a range of numbers that can be a
solution. In that range there is an infinite amount of possible numbers that make the inequality true.
Example:
We know 4 is greater than 3, so is 5, so is 6, so is 7 and 3.1 works also. So does 3.01 and
3.001. So would 3.12 and 3.13… you start to get the picture that it would be impossible
to list all the possible solutions (all the possible numbers that make the inequality
“true”). Since we cannot list all the answers, we express the solution set by graphing on
a number line.
*To graph an inequality, you must do two things. First you must put a circle on the number (in this case, 3).
Second, you must shade to the side of the circle that contains the solution set.
Circle:
Shade:
> and < get an open circle.
Less than (and < )
 Left (think L, L)
> and < get a closed circle.
Greater than (and > )  Right
0
3
0
Graph the inequality:
1)
3
0
2)
3
0
3)
3
4)
Solving and Graphing: Do all the same steps as solving equations to get the x by itself (isolate x). When the
x is by itself, then you can graph the solution set.
5)
6)
7)
8)
THE ONE DIFFERENCE BETWEEN SOVING EQUATIONS AND INEQUALITIES
When you multiply or divide both sides by a negative number, you must turn the inequality sign around.
* When dividing both sides of the inequality by -3, you must turn the inequality
sign around. So, it changes from < to >.
Solve and Graph:
1)
2)
4)
5)
7)
8)
10)
11)
13)
3)
6)
9)
12)
14)
15)
16)
17)
18)
Corrections – Homework Solving Inequalities and Graphing
4)
9)
OR
-8 -7 -6 -5 -4 -3 -2 -1 0
OR
0
14 15 16 17
18 19 20
16)
-8 -7 -6 -5 -4 -3 -2 -1 0
Name_________________________________________________ Date______________ Color___________
Algebra I
Ms. Hahl
Solving & Graphing Inequalities
Directions: Solve the following inequalities and graph the solution.
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
16)
17)
15)
18)
ANSWERS
Solving & Graphing Inequalities
Directions: Solve the following inequalities and graph the solution.
1)
2)
3)
OR
0
9 10 11 12 13 14 15
0123456789
4)
0
-15 -14 -13 -12 -11 -10 -9
5)
15 16 17 18 19 20 21
6)
-15 -14 -13 -12 -11 -10 -9
7)
0
8)
0
0
6 7 8 9 10 11 12
9)
OR
OR
0
10)
8 9 10 11 12 13 14
0
12 13 14 15 16 17 18
11)
0
12)
39 40 41 42 43 44 45
OR
0
7 8 9 10 11 12 13
-33 -32 -31 -30 -29 -27 -28
13)
0
-18 -17 -16 -15 -14 -13 -12
14)
0
15)
OR
OR
-11 -10 -9 -8 -7 -6 -5
16)
0
-3 -2 -1 0
1 2 3
0123456
17)
-7 -6 -5 -4 -3 -2 -1 0
18)
0123456
-21 -20 -19 -18
0
Name ____________________________________________________ Date ____________ Color ____________
Algebra I
Ms. Hahl
Extra Problems
Solving & Graphing Inequalities
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
OR
13)
14)
OR
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
OR
OR
OR
28)
29)
30)
32)
33)
OR
31)
OR
34)
35)
OR
37)
36)
OR
38)
OR
39)
OR
40)
OR
Name _________________________________________________________ Date __________ Color _________
Algebra I
Ms. Hahl
Extra Compound Inequalities
Directions: Solve the following Compound Inequalities and then graph the solution.
1)
2)
3)
4)
5)
6)
7)
8)
ANSWERS
Extra Compound Inequalities
Directions: Solve the following Compound Inequalities and then graph the solution.
1)
2)
0 1
6
0
3)
2
6
4)
0
2
3
-3
0
5)
6)
-12
0
3
-9
0
4
7)
8)
0
-7
0
3
6
9