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 :

                     1/6*(2-p)-3-(p/10)>0 

Step by step solution :

Step  1  :

             p
 Simplify   ——
            10

Equation at the end of step  1  :

    1                      p
  ((— • (2 - p)) -  3) -  ——  > 0 
    6                     10

Step  2  :

            1
 Simplify   —
            6

Equation at the end of step  2  :

    1                      p
  ((— • (2 - p)) -  3) -  ——  > 0 
    6                     10

Step  3  :

Equation at the end of step  3  :

   (2 - p)           p
  (——————— -  3) -  ——  > 0 
      6             10

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  6  as the denominator :

         3     3 • 6
    3 =  —  =  —————
         1       6  

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 :

 4.2       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:

 (2-p) - (3 • 6)     -p - 16
 ———————————————  =  ———————
        6               6   

Equation at the end of step  4  :

  (-p - 16)     p
  ————————— -  ——  > 0 
      6        10

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -p - 16  =   -1 • (p + 16) 

Calculating the Least Common Multiple :

 6.2    Find the Least Common Multiple

      The left denominator is :       6 

      The right denominator is :       10 

      Least Common Multiple:
      30 

Calculating Multipliers :

 6.3    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 = 3

Making Equivalent Fractions :

 6.4      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.      (-p-16) • 5
   ——————————————————  =   ———————————
         L.C.M                 30     

   R. Mult. • R. Num.      p • 3
   ——————————————————  =   —————
         L.C.M              30  

Adding fractions that have a common denominator :

 6.5       Adding up the two equivalent fractions

 (-p-16) • 5 - (p • 3)     -8p - 80
 —————————————————————  =  ————————
          30                  30   

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   -8p - 80  =   -8 • (p + 10) 

Equation at the end of step  7  :

  -8 • (p + 10)
  —————————————  > 0 
       30      

Step  8  :

 8.1    Multiply both sides by  30 

 8.2    Divide both sides by  -8 

Remember to flip the inequality sign:

Solve Basic Inequality :

 8.3      Subtract  10  from both sides

            p < -10

Inequality Plot :

 8.4      Inequality plot for

         -0.267 X  - 2.667  <  0

  
 

One solution was found :