Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "38.75" was replaced by "(3875/100)". 2 more similar replacement(s)

Rearrange:

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

                (1625/100)+(3875/100)*p-(365)≤0 

Step by step solution :

Step  1  :

            155
 Simplify   ———
             4 

Equation at the end of step  1  :

   1625     155          
  (———— +  (——— • p)) -  365  ≤ 0 
   100       4           

Step  2  :

            65
 Simplify   ——
            4 

Equation at the end of step  2  :

   65    155p     
  (—— +  ————) -  365  ≤ 0 
   4      4       

Step  3  :

Adding fractions which have a common denominator :

 3.1       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 65 + 155p     155p + 65
 —————————  =  —————————
     4             4    

Equation at the end of step  3  :

  (155p + 65)    
  ——————————— -  365  ≤ 0 
       4         

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  4  as the denominator :

           365     365 • 4
    365 =  ———  =  ———————
            1         4   

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

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   155p + 65  =   5 • (31p + 13) 

Adding fractions that have a common denominator :

 5.2       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 • (31p+13) - (365 • 4)     155p - 1395
 ————————————————————————  =  ———————————
            4                      4     

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   155p - 1395  =   155 • (p - 9) 

Equation at the end of step  6  :

  155 • (p - 9)
  —————————————  ≤ 0 
        4      

Step  7  :

 7.1    Multiply both sides by  4 

 7.2    Divide both sides by  155 

Solve Basic Inequality :

 7.3      Add  9  to both sides

             p ≤ 9

Inequality Plot :

 7.4      Inequality plot for

         38.750 X  - 348.750  ≤  0

  
 

One solution was found :