Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.98" was replaced by "(198/100)". 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 :

                     h/(75/10)-((198/100))>0 

Step by step solution :

Step  1  :

            99
 Simplify   ——
            50

Equation at the end of step  1  :

  75    99
  —— -  ——  > 0 
  10    50

Step  2  :

            15
 Simplify   ——
            2 

Equation at the end of step  2  :

  15    99
  —— -  ——  > 0 
  2     50

Step  3  :

                15
 Divide  h  by  ——
                2 

Equation at the end of step  3  :

  2h    99
  —— -  ——  > 0 
  15    50

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       15 

      The right denominator is :       50 

      Least Common Multiple:
      150 

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 = 10

   Right_M = L.C.M / R_Deno = 3

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.      2h • 10
   ——————————————————  =   ———————
         L.C.M               150  

   R. Mult. • R. Num.      99 • 3
   ——————————————————  =   ——————
         L.C.M              150  

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:

 2h • 10 - (99 • 3)     20h - 297
 ——————————————————  =  —————————
        150                150   

Equation at the end of step  4  :

  20h - 297
  —————————  > 0 
     150   

Step  5  :

 5.1    Multiply both sides by  150 

 5.2    Divide both sides by  20  

      h-(297/20)  > 0

Solve Basic Inequality :

 5.3      Add  297/20  to both sides

             h > 297/20

Inequality Plot :

 5.4      Inequality plot for

         0.133 h  - 1.980  >  0

  
 

One solution was found :