Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "347.96" was replaced by "(34796/100)". 2 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 :

                (1122/100)*x-200-((34796/100))<0 

Step by step solution :

Step  1  :

            8699
 Simplify   ————
             25 

Equation at the end of step  1  :

    1122                 8699
  ((———— • x) -  200) -  ————  < 0 
    100                   25 

Step  2  :

            561
 Simplify   ———
            50 

Equation at the end of step  2  :

    561                 8699
  ((——— • x) -  200) -  ————  < 0 
    50                   25 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  50  as the denominator :

           200     200 • 50
    200 =  ———  =  ————————
            1         50   

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 :

 3.2       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:

 561x - (200 • 50)     561x - 10000
 —————————————————  =  ————————————
        50                  50     

Equation at the end of step  3  :

  (561x - 10000)    8699
  —————————————— -  ————  < 0 
        50           25 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       50 

      The right denominator is :       25 

      Least Common Multiple:
      50 

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.      (561x-10000)
   ——————————————————  =   ————————————
         L.C.M                  50     

   R. Mult. • R. Num.      8699 • 2
   ——————————————————  =   ————————
         L.C.M                50   

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (561x-10000) - (8699 • 2)     561x - 27398
 —————————————————————————  =  ————————————
            50                      50     

Equation at the end of step  4  :

  561x - 27398
  ————————————  < 0 
       50     

Step  5  :

 5.1    Multiply both sides by  50 

 5.2    Divide both sides by  561  

      x-(27398/561)  < 0

Solve Basic Inequality :

 5.3      Add  27398/561  to both sides

             x < 27398/561

Inequality Plot :

 5.4      Inequality plot for

         11.220 x  - 547.960  <  0

  
 

One solution was found :