COMPOUND INEQUALITY
Definition Of Compound Inequality
Compound Inequality is two or more simple inequalities joined by the terms 'and' or 'or'.
Examples of Compound Inequality
0 ≤ x ≤ 4 is an example of compound inequality, which says that x is either 0 or 4, or any number between 0 and 4.
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y < -13="" or="" y="" ≥="" 10="" is="" a="" compound="" inequality,="" which="" says="" that="" the="" values="" of="" y="" are="" either="" less="" than="" -="" 13="" or="" greater="" than="" or="" equal="" to="">
Video Examples: Compound Inequalities
Solved Example onCompound Inequality
Ques: Choose a compound inequality that represents the set of all real numbers less than or equal to - 7 or greater than or equal to 5.
Choices:
A. x ≤ - 7 or x > 5
B. x < -7="" or="" x="" ≥="">
C. x < -7="" o="" x=""> 5
D. x ≤ -7 or x ≥ 5
Correct Answer: D
Solution:
Step 1: The algebraic model for the statement is x ≤ - 7 or x ≥ 5.
Step 2: The graph of this compound inequality is shown below. Notice that the graph has two parts. One part lies to the left of -7. The other part lies to the right of 5.
Quick Summary
- Compound inequalities involve two or more inequalities.
- They are connected by 'and' or 'or'.
- 'And' means both inequalities must be true.
- 'Or' means at least one inequality must be true.
🍎 Teacher Insights
Use visual aids like number lines to illustrate the solution sets of compound inequalities. Emphasize the difference between 'and' and 'or' using real-world examples.🎓 Prerequisites
- Solving inequalities
- Understanding 'and' and 'or' conditions
- Graphing inequalities on a number line
Check Your Knowledge
Q1: Which compound inequality represents all real numbers less than or equal to -7 or greater than or equal to 5?
Q2: Solve the compound inequality: 2 < x < 5
Frequently Asked Questions
Q: What is the difference between 'and' and 'or' in compound inequalities?
A: 'And' means the solution must satisfy both inequalities simultaneously. 'Or' means the solution must satisfy at least one of the inequalities.
Q: How do you solve a compound inequality with 'and'?
A: Solve each inequality separately, then find the intersection of their solution sets.
Q: How do you solve a compound inequality with 'or'?
A: Solve each inequality separately, then find the union of their solution sets.