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 :

                10*((5/10)*x-2)-(3*x+20+8*x)=0 

Step by step solution :

Step  1  :

            1
 Simplify   —
            2

Equation at the end of step  1  :

          1                
  (10 • ((— • x) -  2)) -  (11x + 20)  = 0 
          2                

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a whole from a fraction

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

         2     2 • 2
    2 =  —  =  —————
         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 :

 2.2       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 - (2 • 2)     x - 4
 ———————————  =  —————
      2            2  

Equation at the end of step  2  :

        (x - 4)     
  (10 • ———————) -  (11x + 20)  = 0 
           2        

Step  3  :

Equation at the end of step  3  :

  5 • (x - 4) -  (11x + 20)  = 0 

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   -6x - 40  =   -2 • (3x + 20) 

Equation at the end of step  5  :

  -2 • (3x + 20)  = 0 

Step  6  :

Equations which are never true :

 6.1      Solve :    -2   =  0

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

Solving a Single Variable Equation :

 6.2      Solve  :    3x+20 = 0 

 Subtract  20  from both sides of the equation : 
                      3x = -20
Divide both sides of the equation by 3:
                     x = -20/3 = -6.667

One solution was found :