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 :

                     p-7/12-(3/10)>0 

Step by step solution :

Step  1  :

             3
 Simplify   ——
            10

Equation at the end of step  1  :

         7      3
  (p -  ——) -  ——  > 0 
        12     10

Step  2  :

             7
 Simplify   ——
            12

Equation at the end of step  2  :

         7      3
  (p -  ——) -  ——  > 0 
        12     10

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  12  as the denominator :

          p     p • 12
     p =  —  =  ——————
          1       12  

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:

 p • 12 - (7)     12p - 7
 ————————————  =  ———————
      12            12   

Equation at the end of step  3  :

  (12p - 7)     3
  ————————— -  ——  > 0 
     12        10

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       12 

      The right denominator is :       10 

      Least Common Multiple:
      60 

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 = 5

   Right_M = L.C.M / R_Deno = 6

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.      (12p-7) • 5
   ——————————————————  =   ———————————
         L.C.M                 60     

   R. Mult. • R. Num.      3 • 6
   ——————————————————  =   —————
         L.C.M              60  

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (12p-7) • 5 - (3 • 6)     60p - 53
 —————————————————————  =  ————————
          60                  60   

Equation at the end of step  4  :

  60p - 53
  ————————  > 0 
     60   

Step  5  :

 5.1    Multiply both sides by  60 

 5.2    Divide both sides by  60  

      p-(53/60)  > 0

Solve Basic Inequality :

 5.3      Add  53/60  to both sides

             p > 53/60

Inequality Plot :

 5.4      Inequality plot for

         p  - 0.883  >  0

  
 

One solution was found :