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Solving Compound Inequalities
After studying this lesson, you will be able to:
Compound inequalities are two inequalities considered together.
A compound inequality containing the word and is true only if both inequalities are true. This type of compound inequality is called a conjunction.
Examples of conjunctions:
x > -5 and x <1
y < 3 and y > -3
A compound inequality containing the word or is true if either of the inequalities is true. This type of compound inequality is called a disjunction.
Examples of disjunctions:
x > -5 or x > 1
y < 3 or y > -3
Therefore, our answer is y> -3 or y <3
(this means that y can be any number since all numbers are either greater than -3 or less than positive 3)
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Therefore, our answer is x < 3 and x > -3 (this means that x must be some number between 3 and -3 )
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Therefore, our answer is m < 2 and m> 1
(this means that x must be some number between 1 and 2 )
2 < 3x + 2 is the first inequality
3x + 2 < 14 is the second inequality
Now, we solve the way we did in Examples 1 -3: 2 < 3x + 2 and 3x + 2 < 14
Therefore, our answer is x> 0 and x <4 or we can write it 0 < x < 4
(this means that x must be some number between 0 and 4 )Buy and download Algebra Buster now and you will also receive 30 minutes of free live tutoring from tutor.com!
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