Solution - Adding, subtracting and finding the least common multiple

Rearrange:

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

                     y+4/5-(1/4)>0 

Step by step solution :

Step  1  :

            1
 Simplify   —
            4

Equation at the end of step  1  :

        4     1
  (y +  —) -  —  > 0 
        5     4

Step  2  :

            4
 Simplify   —
            5

Equation at the end of step  2  :

        4     1
  (y +  —) -  —  > 0 
        5     4

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  5  as the denominator :

          y     y • 5
     y =  —  =  —————
          1       5  

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:

 y • 5 + 4     5y + 4
 —————————  =  ——————
     5           5   

Equation at the end of step  3  :

  (5y + 4)    1
  ———————— -  —  > 0 
     5        4

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       4 

      Least Common Multiple:
      20 

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 = 4

   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.      (5y+4) • 4
   ——————————————————  =   ——————————
         L.C.M                 20    

   R. Mult. • R. Num.       5
   ——————————————————  =   ——
         L.C.M             20

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (5y+4) • 4 - (5)     20y + 11
 ————————————————  =  ————————
        20               20   

Equation at the end of step  4  :

  20y + 11
  ————————  > 0 
     20   

Step  5  :

 5.1    Multiply both sides by  20 

 5.2    Divide both sides by  20  

      y+(11/20)  > 0

Solve Basic Inequality :

 5.3      Subtract  11/20  from both sides

            y > -11/20

Inequality Plot :

 5.4      Inequality plot for

         y  + 0.550  >  0

  
 

One solution was found :