# 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.

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...

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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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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.}

Approved by eNotes Editorial Team