Solution - Linear equations with one unknown

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.5" was replaced by "(5/10)".

Rearrange:

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

                30*((5/10)*x+3)-(20*(x+2))=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

         5
  (30•((——•x)+3))-20•(x+2)  = 0 
        10

Step  2  :

            1
 Simplify   —
            2

Equation at the end of step  2  :

          1                
  (30 • ((— • x) +  3)) -  20 • (x + 2)  = 0 
          2                

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  2  as the denominator :

         3     3 • 2
    3 =  —  =  —————
         1       2  

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

Adding fractions that have a common denominator :

 3.2       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:

 x + 3 • 2     x + 6
 —————————  =  —————
     2           2  

Equation at the end of step  3  :

        (x + 6)     
  (30 • ———————) -  20 • (x + 2)  = 0 
           2        

Step  4  :

Equation at the end of step  4  :

  15 • (x + 6) -  20 • (x + 2)  = 0 

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   50 - 5x  =   -5 • (x - 10) 

Equation at the end of step  6  :

  -5 • (x - 10)  = 0 

Step  7  :

Equations which are never true :

 7.1      Solve :    -5   =  0

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

Solving a Single Variable Equation :

 7.2      Solve  :    x-10 = 0 

 Add  10  to both sides of the equation : 
                      x = 10

One solution was found :