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 :

                     7/10-(1*(5/8)+p)>0 

Step by step solution :

Step  1  :

            5
 Simplify   —
            8

Equation at the end of step  1  :

   7          5     
  —— -  ((1 • —) +  p)  > 0 
  10          8     

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  8  as the denominator :

         p     p • 8
    p =  —  =  —————
         1       8  

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 :

 2.2       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:

 5 + p • 8     8p + 5
 —————————  =  ——————
     8           8   

Equation at the end of step  2  :

   7    (8p + 5)
  —— -  ————————  > 0 
  10       8    

Step  3  :

             7
 Simplify   ——
            10

Equation at the end of step  3  :

   7    (8p + 5)
  —— -  ————————  > 0 
  10       8    

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       8 

      Least Common Multiple:
      40 

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 = 4

   Right_M = L.C.M / R_Deno = 5

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.      7 • 4
   ——————————————————  =   —————
         L.C.M              40  

   R. Mult. • R. Num.      (8p+5) • 5
   ——————————————————  =   ——————————
         L.C.M                 40    

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 7 • 4 - ((8p+5) • 5)     3 - 40p
 ————————————————————  =  ———————
          40                40   

Equation at the end of step  4  :

  3 - 40p
  ———————  > 0 
    40   

Step  5  :

 5.1    Multiply both sides by  40 

 5.2    Multiply both sides by (-1)

Flip the inequality sign since you are multiplying by a negative number

      40p-3  < 0

 5.3    Divide both sides by  40  

      p-(3/40)  < 0

Solve Basic Inequality :

 5.4      Add  3/40  to both sides

             p < 3/40

Inequality Plot :

 5.5      Inequality plot for

         -p  + 0.075  >  0

  
 

One solution was found :