Solution - Adding, subtracting and finding the least common multiple

Rearrange:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

                     4/9*g-3-(7/3)>0 

Step by step solution :

Step  1  :

            7
 Simplify   —
            3

Equation at the end of step  1  :

    4               7
  ((— • g) -  3) -  —  > 0 
    9               3

Step  2  :

            4
 Simplify   —
            9

Equation at the end of step  2  :

    4               7
  ((— • g) -  3) -  —  > 0 
    9               3

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  9  as the denominator :

         3     3 • 9
    3 =  —  =  —————
         1       9  

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:

 4g - (3 • 9)     4g - 27
 ————————————  =  ———————
      9              9   

Equation at the end of step  3  :

  (4g - 27)    7
  ————————— -  —  > 0 
      9        3

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       9 

      The right denominator is :       3 

      Least Common Multiple:
      9 

Calculating Multipliers :

 4.2    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 = 1

   Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

 4.3      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.      (4g-27)
   ——————————————————  =   ———————
         L.C.M                9   

   R. Mult. • R. Num.      7 • 3
   ——————————————————  =   —————
         L.C.M               9  

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (4g-27) - (7 • 3)     4g - 48
 —————————————————  =  ———————
         9                9   

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   4g - 48  =   4 • (g - 12) 

Equation at the end of step  5  :

  4 • (g - 12)
  ————————————  > 0 
       9      

Step  6  :

 6.1    Multiply both sides by  9 

 6.2    Divide both sides by  4 

Solve Basic Inequality :

 6.3      Add  12  to both sides

             g > 12

Inequality Plot :

 6.4      Inequality plot for

         0.444 X  - 5.333  >  0

  
 

One solution was found :