Solution - Linear equations with one unknown

Step by step solution :

Step  1  :

Step  2  :

Pulling out like terms :

 2.1     Pull out like factors :

   4w - 2  =   2 • (2w - 1) 

Equation at the end of step  2  :

  2 • (9 - w) • (2w - 1)  = 0 

Step  3  :

Theory - Roots of a product :

 3.1    A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.

Equations which are never true :

 3.2      Solve :    2   =  0

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

Solving a Single Variable Equation :

 3.3      Solve  :    -w+9 = 0 

 Subtract  9  from both sides of the equation : 
                      -w = -9
Multiply both sides of the equation by (-1) :  w = 9

Solving a Single Variable Equation :

 3.4      Solve  :    2w-1 = 0 

 Add  1  to both sides of the equation : 
                      2w = 1
Divide both sides of the equation by 2:
                     w = 1/2 = 0.500

Two solutions were found :

1.  w = 1/2 = 0.500
   
2.  w = 9