Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.3" was replaced by "(13/10)". 2 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 :

                     (832/100)-((13/10)*n)≥0 

Step by step solution :

Step  1  :

            13
 Simplify   ——
            10

Equation at the end of step  1  :

  832     13
  ——— -  (—— • n)  ≥ 0 
  100     10

Step  2  :

            208
 Simplify   ———
            25 

Equation at the end of step  2  :

  208    13n
  ——— -  ———  ≥ 0 
  25     10 

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       25 

      The right denominator is :       10 

      Least Common Multiple:
      50 

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 = 5

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.      208 • 2
   ——————————————————  =   ———————
         L.C.M               50   

   R. Mult. • R. Num.      13n • 5
   ——————————————————  =   ———————
         L.C.M               50   

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:

 208 • 2 - (13n • 5)     416 - 65n
 ———————————————————  =  —————————
         50                 50    

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   416 - 65n  =   -13 • (5n - 32) 

Equation at the end of step  4  :

  -13 • (5n - 32)
  ———————————————  ≥ 0 
        50       

Step  5  :

 5.1    Multiply both sides by  50 

 5.2    Divide both sides by  -13 

Remember to flip the inequality sign:

 5.3    Divide both sides by  5  

      n-(32/5)  ≤ 0

Solve Basic Inequality :

 5.4      Add  32/5  to both sides

             n ≤ 32/5

Inequality Plot :

 5.5      Inequality plot for

         -1.300 X  + 8.320  ≤  0

  
 

One solution was found :