Solution - Linear equations with one unknown

Rearrange:

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

                     5-10*z-(2*(-7*z/2-1))=0 

Step by step solution :

Step  1  :

            z
 Simplify   —
            2

Equation at the end of step  1  :

                                z      
  (5 - 10z) -  (2 • ((0 -  (7 • —)) -  1))  = 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 :

         1     1 • 2
    1 =  —  =  —————
         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:

 -7z - (2)     -7z - 2
 —————————  =  ———————
     2            2   

Equation at the end of step  2  :

                    (-7z - 2)
  (5 - 10z) -  (2 • —————————)  = 0 
                        2    

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   -7z - 2  =   -1 • (7z + 2) 

Equation at the end of step  4  :

  (5 - 10z) -  (-7z - 2)  = 0 

Step  5  :

Equation at the end of step  5  :

  7 - 3z  = 0 

Step  6  :

Solving a Single Variable Equation :

 6.1      Solve  :    -3z+7 = 0 

 Subtract  7  from both sides of the equation : 
                      -3z = -7
Multiply both sides of the equation by (-1) :  3z = 7


Divide both sides of the equation by 3:
                     z = 7/3 = 2.333

One solution was found :