Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.75" was replaced by "(75/100)". 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 :

                (35/10)*k-(75/100)-(20)>0 

Step by step solution :

Step  1  :

            3
 Simplify   —
            4

Equation at the end of step  1  :

    35         3     
  ((—— • k) -  —) -  20  > 0 
    10         4     

Step  2  :

            7
 Simplify   —
            2

Equation at the end of step  2  :

    7         3     
  ((— • k) -  —) -  20  > 0 
    2         4     

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       4 

      Least Common Multiple:
      4 

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 = 1

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.      7k • 2
   ——————————————————  =   ——————
         L.C.M               4   

   R. Mult. • R. Num.      3
   ——————————————————  =   —
         L.C.M             4

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:

 7k • 2 - (3)     14k - 3
 ————————————  =  ———————
      4              4   

Equation at the end of step  3  :

  (14k - 3)    
  ————————— -  20  > 0 
      4        

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  4  as the denominator :

          20     20 • 4
    20 =  ——  =  ——————
          1        4   

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 :

 4.2       Adding up the two equivalent fractions

 (14k-3) - (20 • 4)     14k - 83
 ——————————————————  =  ————————
         4                 4    

Equation at the end of step  4  :

  14k - 83
  ————————  > 0 
     4    

Step  5  :

 5.1    Multiply both sides by  4 

 5.2    Divide both sides by  14  

      k-(83/14)  > 0

Solve Basic Inequality :

 5.3      Add  83/14  to both sides

             k > 83/14

Inequality Plot :

 5.4      Inequality plot for

         3.500 k  - 20.750  >  0

  
 

One solution was found :