Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

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

                10*((4/10)+(5/10)*g)-(4*g)=0 

Step by step solution :

Step  1  :

            1
 Simplify   —
            2

Equation at the end of step  1  :

          4     1           
  (10 • (—— +  (— • g))) -  4g  = 0 
         10     2           

Step  2  :

            2
 Simplify   —
            5

Equation at the end of step  2  :

         2    g      
  (10 • (— +  —)) -  4g  = 0 
         5    2      

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       2 

      Least Common Multiple:
      10 

Calculating Multipliers :

 3.2    Calculate multipliers for the two fractions


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = 2

   Right_M = L.C.M / R_Deno = 5

Making Equivalent Fractions :

 3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)²   and  (y²+y)/(y+1)³  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

   L. Mult. • L. Num.      2 • 2
   ——————————————————  =   —————
         L.C.M              10  

   R. Mult. • R. Num.      g • 5
   ——————————————————  =   —————
         L.C.M              10  

Adding fractions that have a common denominator :

 3.4       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:

 2 • 2 + g • 5     5g + 4
 —————————————  =  ——————
      10             10  

Equation at the end of step  3  :

        (5g + 4)     
  (10 • ————————) -  4g  = 0 
           10        

Step  4  :

Equation at the end of step  4  :

  (5g + 4) -  4g  = 0 

Step  5  :

Equation at the end of step  5  :

  g + 4  = 0 

Step  6  :

Solving a Single Variable Equation :

 6.1      Solve  :    g+4 = 0 

 Subtract  4  from both sides of the equation : 
                      g = -4

One solution was found :