Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "59.25" was replaced by "(5925/100)". 3 more similar replacement(s)

Rearrange:

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

                (75/100)*n+(15/10)-((5925/100))<0 

Step by step solution :

Step  1  :

            237
 Simplify   ———
             4 

Equation at the end of step  1  :

     75         15     237
  ((——— • n) +  ——) -  ———  < 0 
    100         10      4 

Step  2  :

            3
 Simplify   —
            2

Equation at the end of step  2  :

     75         3     237
  ((——— • n) +  —) -  ———  < 0 
    100         2      4 

Step  3  :

            3
 Simplify   —
            4

Equation at the end of step  3  :

    3         3     237
  ((— • n) +  —) -  ———  < 0 
    4         2      4 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       2 

      Least Common Multiple:
      4 

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 = 1

   Right_M = L.C.M / R_Deno = 2

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.      3n
   ——————————————————  =   ——
         L.C.M             4 

   R. Mult. • R. Num.      3 • 2
   ——————————————————  =   —————
         L.C.M               4  

Adding fractions that have a common denominator :

 4.4       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:

 3n + 3 • 2     3n + 6
 ——————————  =  ——————
     4            4   

Equation at the end of step  4  :

  (3n + 6)    237
  ———————— -  ———  < 0 
     4         4 

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   3n + 6  =   3 • (n + 2) 

Adding fractions which have a common denominator :

 6.2       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:

 3 • (n+2) - (237)     3n - 231
 —————————————————  =  ————————
         4                4    

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   3n - 231  =   3 • (n - 77) 

Equation at the end of step  7  :

  3 • (n - 77)
  ————————————  < 0 
       4      

Step  8  :

 8.1    Multiply both sides by  4 

 8.2    Divide both sides by  3 

Solve Basic Inequality :

 8.3      Add  77  to both sides

             n < 77

Inequality Plot :

 8.4      Inequality plot for

         0.750 X  - 57.750  <  0

  
 

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