6.3 Compound Inequalities

1
6.3 Compound Inequalities

• Objective
• How to solve and graph compound inequalities
• How to model a real life situation with a
  compound inequality

2
Learn to Read

• alt x ltb
• Read x is between a and b
• alt x lt b
• Read x is between a b inclusive

3
Graph 1lt x lt 5
Read as ?
x is between 1 and 5
1
2
3
4
5
6
0
7
4
Write the inequality x greater than 2 or x less
than -1
x lt -1 x gt 2
Graph

-2
-1
0
1
2
3
Remember (closed circle) when the number is
included!
5
Solve Compound Inequalities and Graph
Solve like an equation, but now you have three
parts!
-9 lt 6x 3 39
Subtract 3 from all three parts.
-3
-3
-3
-12 lt 6x 36
Divide each part by 6.
6
6
6
-2 lt x 6
GRAPH
-2
-1
0
1
2
3
4
5
6 7
-3
6
Write the inequality, solve and then graph
Eight plus two times a number is less than six.
8 2x lt 6
-8 -8
2x lt -2

x lt -1
-2
-1
0
1
2
3
7
Write the inequality, solve and then graph
Eight times a number x plus 4 is between -4 and
20.
-4lt 8x 4 lt 20
-4 -4 -4
-8 lt 8x lt 16
-1 lt x lt 2

-2
-1
0
1
2
3
The numbers should be displayed least to greatest
Example you would not write 2 gt x gt -1
8
Use inequalities to solve the following problem.
What are the restriction on the value of x in the
triangle? Remember that two side of a triangle
must add up to be greater than the third
side. You must set up three inequalities!
x
4
x 4 gt 6 x gt 2 x 6 gt 4 x gt -2 length cannot
be negative 6 4 gt x 10 gt x
6
2 lt x lt 10
9
Practice
Graph

1. x gt 4 or x lt -2 2. -2 lt x lt 3
-3 -2
-1
0
1
2
3 4 5

-2
-1
0
1
2
3

• Solve
• 2 x gt 3
• 3 lt 2 - x lt 5

Same thing as.. But line order
5. Write an inequality for the following graph
2 3 4 5 6 7 8 9 10
4 x 8