Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.6" was replaced by "(16/10)". 2 more similar replacement(s)

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                (14/10)*(x+5)+(16/10)*x-(52)=0 

Step by step solution :

Step  1  :

            8
 Simplify   —
            5

Equation at the end of step  1  :

    14                8          
  ((—— • (x + 5)) +  (— • x)) -  52  = 0 
    10                5          

Step  2  :

            7
 Simplify   —
            5

Equation at the end of step  2  :

    7               8x     
  ((— • (x + 5)) +  ——) -  52  = 0 
    5               5      

Step  3  :

Equation at the end of step  3  :

   7 • (x + 5)    8x     
  (——————————— +  ——) -  52  = 0 
        5         5      

Step  4  :

Adding fractions which have a common denominator :

 4.1       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 7 • (x+5) + 8x     15x + 35
 ——————————————  =  ————————
       5               5    

Equation at the end of step  4  :

  (15x + 35)    
  —————————— -  52  = 0 
      5         

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5  as the denominator :

          52     52 • 5
    52 =  ——  =  ——————
          1        5   

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   15x + 35  =   5 • (3x + 7) 

Adding fractions that have a common denominator :

 6.2       Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 (3x+7) - (52)     3x - 45
 —————————————  =  ———————
       1              1   

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   3x - 45  =   3 • (x - 15) 

Equation at the end of step  7  :

  3 • (x - 15)  = 0 

Step  8  :

Equations which are never true :

 8.1      Solve :    3   =  0

This equation has no solution.
A a non-zero constant never equals zero.

Solving a Single Variable Equation :

 8.2      Solve  :    x-15 = 0 

 Add  15  to both sides of the equation : 
                      x = 15

One solution was found :