Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.25" was replaced by "(125/100)". 3 more similar replacement(s)

Rearrange:

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

           (987/100)-((362/100)-(125/100)*n)≥0 

Step by step solution :

Step  1  :

            5
 Simplify   —
            4

Equation at the end of step  1  :

  987     362     5
  ——— -  (——— -  (— • n))  ≥ 0 
  100     100     4

Step  2  :

            181
 Simplify   ———
            50 

Equation at the end of step  2  :

  987     181    5n
  ——— -  (——— -  ——)  ≥ 0 
  100     50     4 

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       50 

      The right denominator is :       4 

      Least Common Multiple:
      100 

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 = 2

   Right_M = L.C.M / R_Deno = 25

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.      181 • 2
   ——————————————————  =   ———————
         L.C.M               100  

   R. Mult. • R. Num.      5n • 25
   ——————————————————  =   ———————
         L.C.M               100  

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:

 181 • 2 - (5n • 25)     362 - 125n
 ———————————————————  =  ——————————
         100                100    

Equation at the end of step  3  :

  987    (362 - 125n)
  ——— -  ————————————  ≥ 0 
  100        100     

Step  4  :

            987
 Simplify   ———
            100

Equation at the end of step  4  :

  987    (362 - 125n)
  ——— -  ————————————  ≥ 0 
  100        100     

Step  5  :

Adding fractions which have a common denominator :

 5.1       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:

 987 - ((362-125n))     125n + 625
 ——————————————————  =  ——————————
        100                100    

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   125n + 625  =   125 • (n + 5) 

Equation at the end of step  6  :

  125 • (n + 5)
  —————————————  ≥ 0 
       100     

Step  7  :

 7.1    Multiply both sides by  100 

 7.2    Divide both sides by  125 

Solve Basic Inequality :

 7.3      Subtract  5  from both sides

            n ≥ -5

Inequality Plot :

 7.4      Inequality plot for

         1.250 X  + 6.250  ≥  0

  
 

One solution was found :