1. 6.3 Solving Compound Inequalities
Objective 1
Write, solve and graph compound inequalities.
Objective 2
Model a real-life situation with a compound inequality.
VOCABULARY
A compound inequality consists of two inequalities connected by the word and or the word or.

2. EX: Graph x > –2 and x < 3
NOTE: Solutions are all numbers that are greater than or equal to –2 and less than 3.
Since X is between –2 and 3 the inequality is usually written as
–2 < X < 3
EX: Graph X < 3 or X > 6
Graph both equations on the same graph

3. Write an inequality that describes each condition.
Example 2
Compound Inequalities in Real Life
Write an inequality that describes each condition.
a. Water is a non-liquid when the temperature is 32°F or below or is at least 212°F.
T ≤ 32 or T ≥ 212
b. A refrigerator is designed to work on an electric line carrying from 115 volts to 120 volts.
115 ≤ V ≤ 120

4. Solving a Compound Inequality with And
Example 3
Solving a Compound Inequality with And
Solve -5 ≤ 2x + 3 < 7. Then graph the solution.
Isolate the variable between the inequality symbols.
–5 ≤ 2x + 3 < 7
Subtract 3 from all three sides
–8 ≤ 2x < 4
Divide each side by 2.
–4 ≤ x < 2
The solution is all real numbers that are greater than or equal to -4 and less than 2.

5. Solving a Compound Inequality with Or
Solve x + 5 < or 3x > 12
Solve each part separately. or
3x >12
x + 5 ≤ –6
x ≤ –11 or
x > 4

6. Solve –3 < –1 – 2x ≤ 5. Then graph the solution.
Example 5
Reversing the sign
Solve –3 < –1 – 2x ≤ 5. Then graph the solution.
–2 < – 2x ≤ 6
Reverse the inequalities when you divide by a negative
– – –2
1 > x ≥ –3

7. Try these Solve and graph the inequality. 1. 2. 3. 4. 2. 3. 4.

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 > 6 x > 2
x + 6 > 4 x > -2 *length cannot be negative*
6 + 4 > x 10 > x 6
2 < x < 10