October 1st
October 1st
Solving Inequalities with Fractions and Parentheses
After studying this lesson, you will be able to:
 Solve inequalities with fractions and parentheses.
Below are the steps for solving inequalities. Remember we are
applying the same rules as we did for equations. If an inequality
contains fractions, the fractions can be cleared out by
multiplying every term in the inequality by the common
denominator. Also, if an inequality contains parentheses, the
parentheses can be removed by using the distributive property.
If we multiply or divide an inequality by a negative, we
reverse the inequality symbol.
The steps for solving inequalities are the same as those for
solving equations:
1. Remove parentheses and clear fractions (if necessary)
2. Collect like terms on each side of the inequality symbol
3. Get the variables together on one side
4. Isolate the variable
5. Check
Example 1

We have a fraction. To clear it, multiply
by the common denominator which is 13 

Multiply each side by the common
denominator 
x > 78 

Check by substituting into the original inequality
Example 2

We have a fraction. To clear it, multiply
by the common denominator which is 4 

Multiply each side by the common
denominator (remember, to reverse the inequality symbol
since we're multiplying by a negative) 
40 <y 
Notice that this can be read "y is
greater than 40" 
Check by substituting into the original inequality
Example 3

We have a fraction. To clear it, multiply
by the common denominator which is 36 

Multiply each side by the common
denominator 
4 (4) < 5r (3) 
Reduce 36 and 9 on the left side to get 4
and reduce 12 and 36 on the right side to get 3. Then, do
the multiplying. 
16 < 15r 


Divide each side by 15 (remember to
reverse the symbol) 


Check by substituting into the original inequality
