Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "10.2" was replaced by "(102/10)".

Rearrange:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

                     a/4-((102/10))<0 

Step by step solution :

Step  1  :

            51
 Simplify   ——
            5 

Equation at the end of step  1  :

  a    51
  — -  ——  < 0 
  4    5 

Step  2  :

            a
 Simplify   —
            4

Equation at the end of step  2  :

  a    51
  — -  ——  < 0 
  4    5 

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       5 

      Least Common Multiple:
      20 

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 = 5

   Right_M = L.C.M / R_Deno = 4

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.      a • 5
   ——————————————————  =   —————
         L.C.M              20  

   R. Mult. • R. Num.      51 • 4
   ——————————————————  =   ——————
         L.C.M               20  

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:

 a • 5 - (51 • 4)     5a - 204
 ————————————————  =  ————————
        20               20   

Equation at the end of step  3  :

  5a - 204
  ————————  < 0 
     20   

Step  4  :

 4.1    Multiply both sides by  20 

 4.2    Divide both sides by  5  

      a-(204/5)  < 0

Solve Basic Inequality :

 4.3      Add  204/5  to both sides

             a < 204/5

Inequality Plot :

 4.4      Inequality plot for

         0.250 a  - 10.200  <  0

  
 

One solution was found :