Algebra 1 Solving Compound Inequalities

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.