3.6 Compound Inequalities
3.6: Compound Inequalities
•Compound inequality: an inequality that
consists of two distinct inequalities, joined
by the word “and” or “or”
“and” compound inequalities
• Solutions need to make BOTH parts of the inequality true
• Ex: −2 < 𝑥 < 5
• If a number is to be a solution, it has to be greater than -2 AND be less than 5
-2
0
5
(−2, 5)
Solving “and” compound inequalities
• You want to get the variable isolated in the middle of
the inequality
• You follow reverse order of operations to move pieces
OUT of the middle (NOT THE VARIABLE)
• If you do an operation to the middle of the inequality,
you have to do the same operation to the other two
sides
Solving “and” compound inequalities
• Solve the following compound inequality
−3 < 𝑚 − 4 < −1
Solving “and” compound inequalities
• Solve the following compound inequality
−3 < −2𝑥 + 5 < 9
“or” compound inequalities
• Solutions need to make ONLY ONE part of the inequality true
• Ex: 𝑥 < 0 or 𝑥 > 3
• If a number is to be a solution, it can either be less than zero OR
greater than 3
0
3
(−∞, 0) and (3, ∞)
Solving “or” compound inequalities
• You solve each part of an or inequality SEPARATELY
• Solve like a basic one-, two-, or multi-step inequality
• If you do an operation to one of the inequalities, you do
NOT do the exact same operation to the other
• Solutions only need to make one of the inequalities
true
Solving “or” compound inequalities
• Solve the following compound inequality
-2𝑦 + 7 ≥ 1 or 4𝑦 + 3 ≤ −5
Solving “or” compound inequalities
• Solve the following compound inequality
5𝑥 ≥ 10 or 3𝑥 + 1 ≤ 7
Weird Answer Inequalities…
• Don’t always assume once you’ve solved an
inequality, that you just leave the answer as issometimes we only use a part of it, sometimes
we have no solution, and sometimes we have
infinitely many solutions
Weird Answer Inequalities…
• Try solving the following 4 inequalities:
1. −4 ≤
3
− 𝑥
4
+ 11 > 14
2. 10𝑥 + 3 ≥ −7 or −1 < 𝑥 − 9
3. 19 ≤ 4 − 3𝑥 < 1
4. 12 − 3𝑥 < 33 or −18 < −2 − 4𝑥
Weird Answer Inequalities…
• Your answers should be…
1. −4 < 𝑥
2. 𝑥 ≥ −1
3. No Solution
4. Infinite Solutions
Compound Inequality Word Problems
• You scored a 78%, 78%, and an 81% on your last
three tests in class. Assuming your grade in the
class is the average of your test scores, what
scores should you get in order to earn an 80% to
an 85% in class?
Practice Problems
• P. 220 #7, 11, 12, 15, 20, 21, 22, 23, 26, 28