You can help keep this site free, by visiting our sponsor, Algebrator - an incredible software program that provides step - by - step solution to not only equations but to any other algebra problem as well!
home
solving equations with fractions
methods for solving quadratic equations
solving equations
solving equations
linear equations
solving equations
solving equations with variables on each side
solving equations
linear equations
solving linear equations
steps for solving linear equations
solving equations with variables on each side
solving quadratic equations
solving equations
solving equations
steps for solving linear equations
quadratic equations
writing linear equations
solving equations
solving rational equations
solving equations
solving equations
solving systems of equations using elimination
solving linear equations
solving equations
solving quadratic equations
methods for solving quadratic equations
solving equations
solving equations
equation solving resources
Try the Free Math Solver or Scroll down to Tutorials!

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


When fractions occur we can sometimes transform the equation to one that does not involve fractions.

Example

Find the solution to the equation

(4 x/ 5) - (7 / 4) = ( x/ 5) + ( x/ 4) .

Solution

The least common multiple of the denominators in the equation is 4 × 5 = 20 and we proceed as follows:

16 x - 35 = 4 x + 5 x

16 x - 35 = 9 x

adding 35 to both sides and subtracting 9 x from both sides leads to

7 x = 35 so x = 5 is the solution to the equation .

Exercise

Find the solution to each of the following equations.

(a) 5 x - 6( x - 5) = 2( x + 5) + 5( x - 4)

(b) ( x + 15)( x - 3) - ( x - 6 x + 9) = 30 - 15( x - 1)

(c) ( x - 2) / 2 + ( x + 10) / 9 = 5

Solution

(a)

5 x - 6( x - 5) = 2( x + 5) + 5( x - 4)

5 x - 6 x + 30 = 2 x + 10 + 5 x - 20

- x + 30 = 7 x - 10

30 = x + 7 x - 10

30 = 8 x - 10

30 + 10 = 8 x

8 x = 40

x = 5

(b) First, using FOIL , we expand

( x + 15)( x - 3) = x - 3 x + 15 x - 45 = x + 12 x - 45

Now we have

( x + 15)( x - 3) - ( x14 2 - 6 x + 9) = 30 - 15( x - 1)

x + 12 x - 45 - x + 6 x - 9 = 30 - 15 x + 15

18 x - 54 = 45 - 15 x

18 x + 15 x - 54 = 45

33 x - 54 = 45

33 x = 45 + 54

33 x = 99

x = 3

(c) This time we multiply both sides by 2 × 9 .

9( x - 2) + 2( x + 10) = 90

9 x - 18 + 2 x + 20 = 90

11 x + 2 = 90

11 x = 88

x = 8

Quiz

Which of the following is the solution to the equation (x - 4)/7 = (x - 10)/5 ?

(a) 11 (b) - 10 (c) 19 (d) 25

Solution:

The highest common factor of the denominators is 5 × 7 = 35 . Multiplying both sides of the equation by this

5( x - 4) = 7( x - 10)

5 x - 20 = 7 x - 70

5 x - 20 + 70 = 7 x - 70 + 70

5 x + 50 = 7 x

50 = 7 x - 5 x = 2 x

x = 25

so that x = 25 is the solution. This can be checked by putting this value into the original equation and showing that each side will have the value 3 .