COMPOUND+INEQUALITIES

Compound Inequlities:

There are two types of Compound Inequalities. Conjunctions: Two inequalities are joined by the word AND. This means that both inequalities must be true.

So if...

x > 3 and x < 5

Then x must be both greater than 3 and less than 5.

Disjunctions: Two inequalities are joined by the word OR. This means that either one of the inequalities could be true.

So if...

x > 3 or x < -2 Then x must be a number greater than 3, or a number less than -2.

On a number line, a disjunction looks like:



The number line shows that x is less than or equal to 3, or greater than for. Notice that an open circle in not inclusive (> or <) and closed circles are inclusive (≤ or ≥ )

 Solving Compound Inequalities: -4 < 2x + 8 ≤ 12

To solve, first, split the conjunction into two seperate inequalities.

-4 < 2x+8 and 2x + 8 ≤ 12

Solve each inequality:

-4 < 2x + 8

-12 < 2x

x > -6

2x + 8 ≤ 12

2x ≤ 4

x ≤ 2

So x > -6 and x ≤ 2

To graph this on a number line, you'd stick a solid dot on 2, and a open dot on -6, and you'd connect them, since it is a conjunction.