Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.7" was replaced by "(27/10)". 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 :

                (149/10)*(v)*(392/10)-((27/10))>0 

Step by step solution :

Step  1  :

            27
 Simplify   ——
            10

Equation at the end of step  1  :

    149        392     27
  ((——— • v) • ———) -  ——  > 0 
    10         10      10

Step  2  :

            196
 Simplify   ———
             5 

Equation at the end of step  2  :

    149        196     27
  ((——— • v) • ———) -  ——  > 0 
    10          5      10

Step  3  :

            149
 Simplify   ———
            10 

Equation at the end of step  3  :

    149        196     27
  ((——— • v) • ———) -  ——  > 0 
    10          5      10

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       25 

      The right denominator is :       10 

      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 = 2

   Right_M = L.C.M / R_Deno = 5

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.      14602v • 2
   ——————————————————  =   ——————————
         L.C.M                 50    

   R. Mult. • R. Num.      27 • 5
   ——————————————————  =   ——————
         L.C.M               50  

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:

 14602v • 2 - (27 • 5)     29204v - 135
 —————————————————————  =  ————————————
          50                    50     

Equation at the end of step  4  :

  29204v - 135
  ————————————  > 0 
       50     

Step  5  :

 5.1    Multiply both sides by  50 

 5.2    Divide both sides by  29204  

      v-(135/29204)  > 0

Solve Basic Inequality :

 5.3      Add  135/29204  to both sides

             v > 135/29204

Inequality Plot :

 5.4      Inequality plot for

         584.080 v  - 2.700  >  0

  
 

One solution was found :