Compound Inequalities with "And"
This page focuses on compound inequalities joined by "and" in Algebra 1. When two inequalities are connected with "and", it restricts the solution to the intersection of both sets.
Definition: A compound inequality joined by "and" includes only solutions that satisfy both of the individual inequalities simultaneously.
To solve and graph "and" inequalities:
- Solve each inequality separately
- Find the overlap or intersection of the solutions
- Graph the resulting bounded region on the number line
Example: Solve and graph -3x + 12 > 6 and 4x + 3 > -13
Solution: x < 2 and x > -4, which simplifies to -4 < x < 2
Graph: Points between -4 and 2 (not including -4) are shaded.
Highlight: "And" inequalities often result in a bounded region, restricting the solution between two values.
The page introduces a more compact notation for "and" inequalities:
Example: Solve and graph -3 < 2x - 1 ≤ 13
Vocabulary: Bounding - A mathematical term meaning to restrict a graph between two values.
Quote: "If your inequality can't go higher than a number and it can't be smaller than a number, it's most likely an 'and' compound inequality."
This concept is crucial for Understanding compound inequalities in Algebra 1 and provides essential Tips for graphing inequalities with AND and OR.
