August 24th
August 24th
Solving Compound Inequalities
After studying this lesson, you will be able to:
 Solve compound inequalities.
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.
Get a PDF of similar solved problems sent to you!
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
Example 1
2y > y  3 or 3y < y + 6 
This is a disjunction (it has the word or
). To solve, we work as two separate inequalities 
2y > y  3 
subtract y from each side 
3y < y + 6 
subtract y from each side 
y > 3 

2y <6 
divide each side by 2 
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)
Algebra Buster software can easily solve any algebra problem
including
compound inequalities such as this one.
See how Algebra Buster solves a similar problem
Example 2
x  4 < 1 and x + 4 > 1 
This is a conjunction (it has the word
and ). To solve, we work as two separate inequalities 
x  4 < 1 
add 4 to each side 
x + 4 > 1 
subtract 4 from each side 
x < 3 

x > 3 

Therefore, our answer is x < 3 and x > 3 (this means
that x must be some number between 3 and 3 )
Algebra Buster software will show you all the steps and explanations
if you need them. Here are
some examples. Our software actually helps you
learn Algebra so there is no need to hire an expensive tutor.
Example 3
3m > m + 4 and 2m + m  6 
This is a conjunction (it has the word
and ). To solve, we work as two separate inequalities 
3m < m + 4 
subtract m from each side 
2m < 4m  6 
subtract 4m from each side 
2m < 4 
divide each side by 2 
6m < 6 
divide each side by 6 (remember to
reverse the symbol) 
m < 2 

m > 1 

Therefore, our answer is m < 2 and m> 1
(this means that x must be some number between 1 and 2 )
Example 4
2 < 3x + 2 < 14 
This is another way to write a
conjunction. There is no word and there are two
inequality symbols. To solve, we break it down to two
inequalities this way: 
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
2 < 3x + 2 
subtract 2 from each side 
3x + 2 < 14 
subtract 2 from each side 
0 < 3x 
divide each side by 3 
3x < 12 
divide each side by 3 
0 < x 

x < 4 

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!
