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Compound Inequalities, Lecture notes of Chemistry

Gonzaga UniversityChemistry

5xа≤а10 or 3xана2 > 4ааis a compound or. • the goal is to find the union of the two answer sets. 17 < x + 3 < 10 is a double inequality that is equivalent to.

Typology: Lecture notes

2022/2023

Uploaded on 02/28/2023

mortimer
mortimer 🇺🇸

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bg1
CompoundInequalities
1
Jan41:42PM
CompoundInequalities
Intersectionoftwosets:
Theelementsthatbothsetshaveincommon.
Theword
"and"
typicallyimpliesintersection.Themathematical
symbolforintersectionis
∩
.
Unionoftwosets:
Alltheelementsthatoccurinatleastoneofthetwo
sets.Theword
"or"
typicallyimpliesunion.Themathematicalsymbol
forunionis
∪
.
Activity:Findtheunionandintersectionofeachpairofsets.
{4,5,8,9,13},{2,4,6,9,12}
{x|x>5},{x|x<12}
{x|x
≥
4},{x|x
≤
5}
Aug54:08PM
compoundinequality
aninequalitythatputsmorethan
oneconditiononthevariable.Forexample:
2x+1>7andx9
≥
6isacompound"and"
•
thegoalistofindtheintersectionofthetwoanswersets.
5x
≤
10or3x2>4isacompound"or"
•
thegoalistofindtheunionofthetwoanswersets.
17<x+3<10isadoubleinequalitythatisequivalentto
thiscompound"and":17<x+3andx+3<10.
•
thegoalofthistypeofinequality,istogetxinthemiddle.
pf3

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Jan 41:42 PM Compound Inequalities Intersection of two sets: The elements that both sets have in common. The word "and" typically implies intersection. The mathematical symbol for intersection is (^) ∩. Union of two sets: All the elements that occur in at least one of the two sets. The word "or" typically implies union. The mathematical symbol for union is (^) ∪. Activity: Find the union and intersection of each pair of sets. {4, 5, 8, 9, 13}, {2, 4, 6, 9, 12} {x| x > 5}, {x| x < 12} {x| x (^) ≥ 4}, {x| x (^) ≤ 5} Aug 54:08 PM compound inequality an inequality that puts more than one condition on the variable. For example: 2x + 1 > 7 and x (^9) ≥ 6 is a compound "and"

  • the goal is to find the intersection of the two answer sets. 5x (^) ≤ 10 or 3x 2 > 4 is a compound "or"
  • the goal is to find the union of the two answer sets. 17 < x + 3 < 10 is a double inequality that is equivalent to this compound "and": 17 < x + 3 and x + 3 < 10.
  • the^ goal^ of^ this^ type^ of^ inequality,^ is^ to^ get^ x^ in^ the^ middle.

Aug 54:34 PM Steps to solve a compound inequality:

  1. Solve each inequality separately.
  2. Graph the solution set of each inequality on the same number line.
  3. Compound "and"...determine the intersection of the solution sets. Compound "or"...determine the union of the solutions sets.
  4. Express the answer in interval notation.
  • A double inequality may be solved by rewriting it as a compound "and" and then following the steps above, or by solving it so that only x remains in the middle. Aug 54:49 PM Activity: Solve the following compound inequality and express the answer in interval notation: 2x + 5 > 1 and 2x + (^4) ≤ 16