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1.4 “solving linear inequalities”. ex 1:. Graph x > 3. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10. ex 1:. Graph x > 3.
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1.4 “solving linear inequalities”
ex 1: Graph x > 3 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
ex 1: Graph x > 3 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
ex 1: Graph x > 3 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 “All real numbers greater than three”
ex 2: Graph x –2 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
ex 2: Graph x –2 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
ex 2: Graph x –2 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 “All real numbers less than or equal to negative two”
ex 3: Solve 5x – 8 < 12
ex 3: Solve 5x – 8 < 12 +8 +8
ex 3: Solve 5x – 8 < 12 +8 +8 5x < 20
ex 3: Solve 5x – 8 < 12 +8 +8 5x < 20 5 5
ex 3: Solve 5x – 8 < 12 +8 +8 5x < 20 5 5 x < 4
ex 3: Solve 5x – 8 < 12 +8 +8 5x < 20 5 5 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x < 4
ex 3: Solve 5x – 8 < 12 +8 +8 5x < 20 5 5 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x < 4
ex 4: Solve –3x 12
ex 4: Solve –3x 12 –3 –3
ex 4: Solve –3x 12 –3 –3 x –4
ex 4: Solve –3x 12 –3 –3 x –4 rule: When you multiply or divide by a negative , the inequality sign switches direction.
ex 5: Solve 2x + 1 6x – 23
ex 5: Solve 2x + 1 6x – 23 –2x –2x
ex 5: Solve 2x + 1 6x – 23 –2x –2x 1 4x – 23
ex 5: Solve 2x + 1 6x – 23 –2x –2x 1 4x – 23 +23 +23
ex 5: Solve 2x + 1 6x – 23 –2x –2x 1 4x – 23 +23 +23 24 4x
ex 5: Solve 2x + 1 6x – 23 –2x –2x 1 4x – 23 +23 +23 24 4x 4 4
ex 5: Solve 2x + 1 6x – 23 –2x –2x 1 4x – 23 +23 +23 24 4x 4 4 6 x
ex 5: Solve 2x + 1 6x – 23 –2x –2x 1 4x – 23 +23 +23 24 4x 4 4 6 x VARIABLES ON THE LEFT-SIDE !
ex 5: Solve 2x + 1 6x – 23 –2x –2x 1 4x – 23 +23 +23 24 4x 4 4 6 x VARIABLES ON THE LEFT-SIDE ! x 6
ex 6: Graph x > –5 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
ex 6: Graph x > –5 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
ex 6: Graph x > –5 Graph x < 7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
ex 6: Graph x > –5 Graph x < 7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
ex 6: Graph x > –5 Graph x < 7 Graph x > –5 and x < 7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
ex 6: Graph x > –5 Graph x < 7 Graph x > –5 and x < 7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
compound inequality Two simple inequalities joined by “and” or “or”
compound inequality Two simple inequalities joined by “and” or “or” x > –5 and x < 7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
compound inequality Two simple inequalities joined by “and” or “or” x > –5 and x < 7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
compound inequality Two simple inequalities joined by “and” or “or” x > –5 and x < 7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 “All real #s that are greater than negative five and less than seven”
compound inequality Two simple inequalities joined by “and” or “or” x > –5 and x < 7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 “All real #s that are greater than negative five and less than seven” –5 < x < 7
compound inequality Two simple inequalities joined by “and” or “or”
compound inequality Two simple inequalities joined by “and” or “or” x < –5 or x >7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
compound inequality Two simple inequalities joined by “and” or “or” x < –5 or x >7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
compound inequality Two simple inequalities joined by “and” or “or” x < –5 or x >7 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 “All real #s that are less than negative five or greater than seven”
ex 7: Solve –2 3x – 8 4
ex 7: Solve –2 3x – 8 4 +8 +8 +8
ex 7: Solve –2 3x – 8 4 +8 +8 +8 6 3x 12
ex 7: Solve –2 3x – 8 4 +8 +8 +8 6 3x 12 3 3 3
ex 7: Solve –2 3x – 8 4 +8 +8 +8 6 3x 12 3 3 3 2 x 4
ex 7: Solve –2 3x – 8 4 +8 +8 +8 6 3x 12 3 3 3 2 x 4 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x 2 and x 4
ex 7: Solve –2 3x – 8 4 +8 +8 +8 6 3x 12 3 3 3 x 2 and x 4 2 x 4 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10