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analytical inequalities Create a compound, first degree inequality  using the connective word AND and another compound inequality using the connective word OR. Solve each of them, and write each solution set in INTERVAL NOTATION.

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Using AND you might get:

(1) a line segment on a graph, or a solution of the form (a,b) Ex x>2 and x<4 often written 2<x<4 with solution (2,4)

(2)a ray on the graph or an infinite set like (a,inf) Ex x>2 and x>4 with solution (4,inf)

(3)or no solution Ex x>2 and x<2

Using OR you might get

(1) Two opposite rays on the graph Ex x<-2 or x>4 with solution (-inf,-2)U(4,inf)

(2) The entire line Ex x<2 or x>1 with solution (-inf,inf)

(3) All but one point Ex X<2 or x>2 with solution (-inf,2)U(2,inf)

Change the strict inequalities to inclusive inequalities and you change the intervals from (a,b) to [a,b], etc...

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Tushar Chandra eNotes educator | Certified Educator

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An example of a compound, first degree inequality using the connective word AND is: What is x such that 2x + 5 > 0 and x + 2 < 0

The solution of this inequality is x > -5/2 and x < -2. x lies in the set {-2.5, -2}

An example of a compound inequality using the connective word OR is: What is x such that x + 4 > 0 or 2x - 1 < 0

The solution of this inequality is x > -4 or x < 1/2. As x can take all values above -4 and all values below 1/2, the solution of the equation is {-inf., inf.}

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