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 :

                     10/3*p-(8/9)>0 

Step by step solution :

Step  1  :

            8
 Simplify   —
            9

Equation at the end of step  1  :

   10         8
  (—— • p) -  —  > 0 
   3          9

Step  2  :

            10
 Simplify   ——
            3 

Equation at the end of step  2  :

   10         8
  (—— • p) -  —  > 0 
   3          9

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       3 

      The right denominator is :       9 

      Least Common Multiple:
      9 

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 = 3

   Right_M = L.C.M / R_Deno = 1

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.      10p • 3
   ——————————————————  =   ———————
         L.C.M                9   

   R. Mult. • R. Num.      8
   ——————————————————  =   —
         L.C.M             9

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:

 10p • 3 - (8)     30p - 8
 —————————————  =  ———————
       9              9   

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   30p - 8  =   2 • (15p - 4) 

Equation at the end of step  4  :

  2 • (15p - 4)
  —————————————  > 0 
        9      

Step  5  :

 5.1    Multiply both sides by  9 

 5.2    Divide both sides by  2 

 5.3    Divide both sides by  15  

      p-(4/15)  > 0

Solve Basic Inequality :

 5.4      Add  4/15  to both sides

             p > 4/15

Inequality Plot :

 5.5      Inequality plot for

         3.333 X  - 0.889  >  0

  
 

One solution was found :