Name: ____________________________________ Period: _____
Packet 20: Solving Fractional Equations
We want to “get rid” of the denominators!
Step 1: Find the least common denominator for the equation
Step 2: Multiply every term in the equation by the least common denominator
Step 3: Reduce each term to create a “denominator free” equation
Step 4: Solve for the variable using the steps to solve an equation
Example:
x 3x 7


10 5 2
Step 1: Find the least common denominator
The least common denominator is _______
Step 2: Multiply every term in the equation by the least common denominator
 _____ 
x
3x
7
  _____ 
  _____ 
10
5
2
Step 3: Reduce each term to create a “denominator free” equation
Step 4: Solve for the variable using the steps to solve an equation
1
Let’s Try It!
Remember to follow the four steps
4x x

3
6
(1)
12 
(2)
4y 2y

 10
9
3
(3)
x 2x 7


3 5 15
2
Fractional Equations Practice
Follow the four steps to solve the following equations. Show all of your work!
5x x 51
x  3 3x



7
1)
2)
8 12 24
5
10
3)
x 4 x
 6
4
3
5)
x
x
3 
4
3
4)
3
y5
 4  16
3
Fractional Equations Homework
Follow the four steps from class to solve the equations below. Show all of your work and make
sure to put a box around your answer.
2x  4
2x  4
6  8
 81
1)
2) 9 
5
3
3)
x 4x

 1
1 3
4)
5)
x
x
 4  3 
4
2
6) r 
4
5x
 9  31
4
r 6
6
9
If there is
only 1 fraction in the equation:
1st: Multiply EVERY piece of the equation by the denominator of that fraction.
2nd: The fraction will disappear and you can proceed as usual!
1)
x
 9  11
5
2)
If there are
x
 4  5
3
3)
2
x  16  64
3
2 or more fractions
in the equation:
1st: Find the Least Common Denominator (LCD) of all of the denominators
2nd: Multiply EVERY piece of the equation by the LCD
*Remember to put all (binomials in parentheses) before multiplying!
3 : Simplify and solve!
rd
LCD: ___
4)
x
5

x
7
 12
LCD: ___
5)
7x
10

x
5
3
2

LCD: ___
6)
5
4
x
2


LCD: ___
5)
x  3
6

x  25
5
 4
7
6
LCD: ___
6)
x  5
2
☼ Make sure you distribute and watch out for the negative!
5

x  1
2

x  1
3
1)
x
 10  1
4
4)
x
3
7)
3x
2
x
6


 2
3
10

1
5
2)
x
- 8 = 15
7
5)
x
3

x
7
 10
8) 10x  3  3x  3   1
10
5
6
10
3)
3
x7  8
4
6)
7x
8
9)
1x
11
4
3x



5
3
3
5

3x
8
 1
Fractional Equations Homework
1)
x
 3  5
6
3)
2x
1x

 22
3
4
5)
x  3
3x

 7
5
10
2)
LCD: ___
7) Solve for x:
5x – (x + 3) = 7 + 2(x + 2)
x
+ 21 = 14
8
4)
2x
x
=9 
5
2
6)
3x
5x
1

 
4
8
2
8) Using order of operations, evaluate:
3[4 – 8 + 42(2 + 5)]
7
9) Perform the indicated
answer in scientific notation:
operation and express your
4.2  102
7  105
_________________________
Match each equation with the property it illustrates.
Properties may be used more than once!
___10) 6 + (10 + 8) = (6 + 10) + 8
___11) 6 + 10 = 10 + 6
___12) –10 + 0 = –10
___13)
10
5
•
 1
5
10
A) Additive Identity
B) Additive Inverse
C) Associative Property
___14) 7(x – 13) = 7x – 91
D) Commutative Property
___15) 0 + 16 = 16
E) Distributive Property
___16) 20 + (–20) = 0
F) Multiplicative Identity
___17) 3(2) = 2(3)
G) Multiplicative Inverse
___18) 5(6 • 3) = (5 • 6)3
8
1. − 8x − 2 = − 26
2. − 1.5 = 0.5x + 7
3. ( 5x + 1 ) – ( 2x – 6 ) = 7
4. 6x + 1
5. 3 ( 2x – 1 ) = 7x + 2
6. 4x − ( 6x – 8 ) = x + 18
9
3x − 10 = − 63
7.
9.
+ 6 = 8
−
−
8.
= − 17
10.
10
= 2
+
=