Ch3_Inequalities_Sections3.1-3.2 - Chapter 3 Inequalities...

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Chapter 3, “Inequalities” from Beginning and Intermediate Algebra by Tyler Wallace is available under a Creative Commons Attribution 3.0 Unported license. © 2010.
3.1Inequalities - Solve and Graph InequalitiesObjective: Solve, graph, and give interval notation for the solution tolinear inequalities.When we have an equation such asx= 4we have a specific value for our variable.With inequalities we will give a range of values for our variable. To do this wewill not use equals, but one of the following symbols:>Greater thangreaterorequalslantGreater than or equal to<Less thanlessorequalslantLess than or equal toWorld View Note:English mathematician Thomas Harriot first used the abovesymbols in 1631. However, they were not immediately accepted as symbols suchasandwere already coined by another English mathematician, WilliamOughtred.If we have an expression such asx <4, this means our variable can be any numbersmaller than 4 such as2,0,3,3.9 or even 3.999999999 as long as it is smaller118
Example 151.Graph the inequality and give the interval notationx <2Start at2and shade belowUse)for less thanOur Graph(− ∞,2)Interval NotationExample 152.Graph the inequality and give the interval notationygreaterorequalslant1Start at1and shade aboveUse[for greater than or equalOur Graph[1,)Interval NotationWe can also take a graph and find the inequality for it.119
Example 153.Give the inequality for the graph:Graph starts at 3 and goes up or greater. Curved bracket means just greater thanx >3Our Solution

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