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 :

                     1/3+b-(3/4)>0 

Step by step solution :

Step  1  :

            3
 Simplify   —
            4

Equation at the end of step  1  :

   1          3
  (— +  b) -  —  > 0 
   3          4

Step  2  :

            1
 Simplify   —
            3

Equation at the end of step  2  :

   1          3
  (— +  b) -  —  > 0 
   3          4

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  3  as the denominator :

         b     b • 3
    b =  —  =  —————
         1       3  

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:

 1 + b • 3     3b + 1
 —————————  =  ——————
     3           3   

Equation at the end of step  3  :

  (3b + 1)    3
  ———————— -  —  > 0 
     3        4

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       3 

      The right denominator is :       4 

      Least Common Multiple:
      12 

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 = 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.      (3b+1) • 4
   ——————————————————  =   ——————————
         L.C.M                 12    

   R. Mult. • R. Num.      3 • 3
   ——————————————————  =   —————
         L.C.M              12  

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (3b+1) • 4 - (3 • 3)     12b - 5
 ————————————————————  =  ———————
          12                12   

Equation at the end of step  4  :

  12b - 5
  ———————  > 0 
    12   

Step  5  :

 5.1    Multiply both sides by  12 

 5.2    Divide both sides by  12  

      b-(5/12)  > 0

Solve Basic Inequality :

 5.3      Add  5/12  to both sides

             b > 5/12

Inequality Plot :

 5.4      Inequality plot for

         b  - 0.417  >  0

  
 

One solution was found :