Algebra 1 Solving Compound Inequalities

Study Notes

Solving Compound Inequalities

Compound inequalities can be expressed in two forms: "and" (conjunction) or "or" (disjunction).
"And" includes values satisfied by both inequalities, while "or" includes values satisfying at least one inequality.

Card Breakdown

Card 1
- Compound inequality: -2 ≤ x < -1
- Equivalent expression: -5 < -6 - x ≤ -4, showing the relationship of x with other numbers.
Card 2
- Compound inequality: x > 6 or x ≤ -6
- Equivalent expression: -9 + x > -3 or x/6 ≤ -1, demonstrating two separate ranges for x.
Card 3
- Compound inequality: x ≤ 3 or x > 9
- Equivalent expression: x + 6 ≤ 9 or x + 2 > 11, which splits the number line into distinct sections.
Card 4
- Compound inequality: x > 1 or x ≤ -7
- Equivalent expression: x + 1 > 2 or x + 7 ≤ 0, indicating two ranges for solution sets.
Card 5
- Compound inequality: 1 ≤ x < 9
- Equivalent expression: -27 < -3x ≤ -3, showing x within a particular interval framed by limits.
Card 6
- Compound inequality: -10 ≤ x ≤ -2
- Equivalent expression: 3x ≥ -30 and x/2 ≤ -1, establishing bounds on x.
Card 7
- Compound inequality: 7 < x < 10
- Equivalent expression: 7 < 2x - 7 < 13, forming a narrow range for x.
Card 8
- Compound inequality: x ≤ -6 or x > 1
- Equivalent expression: 3x - 8 ≤ -26 or -7x + 8 < 1, emphasizing two distinct solution sets.
Card 9
- Compound inequality: x ≤ -9 or x > -3
- Equivalent expression: 5 + 2x ≤ -13 or 8x + 8 > -16, delineating solutions through separate inequalities.
Card 10
- Compound inequality: 2 ≤ x ≤ 8
- Equivalent expression: 6 + 10x ≤ 86 and -9x - 3 ≤ -21, defining finite bounds on x.
Card 11
- Compound inequality: x ≤ -7 or x ≥ -3
- Equivalent expression: 9 + 8x ≤ -47 or -x - 9 ≤ -6, identifying intervals for x based on separate conditions.
Card 12
- Compound inequality: x ≤ -10 or x ≥ 0
- Equivalent expression: 6x - 10 ≤ -70 or 3 - 6x ≤ 3, segmenting x into isolated ranges based on its comparison to numerical values.

Description

Test your understanding of compound inequalities with this interactive flashcard quiz on Algebra 1. Each card presents inequalities for you to solve or define, enhancing your skills in recognizing and solving such mathematical expressions.