Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "8.29" was replaced by "(829/100)". 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 :

                b-(995/100)-(-(829/100))>0 

Step by step solution :

Step  1  :

            829
 Simplify   ———
            100

Equation at the end of step  1  :

        995           829
  (b -  ———) -  (0 -  ———)  > 0 
        100           100

Step  2  :

            199
 Simplify   ———
            20 

Equation at the end of step  2  :

        199     -829
  (b -  ———) -  ————  > 0 
        20      100 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  20  as the denominator :

          b     b • 20
     b =  —  =  ——————
          1       20  

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:

 b • 20 - (199)     20b - 199
 ——————————————  =  —————————
       20              20    

Equation at the end of step  3  :

  (20b - 199)    -829
  ——————————— -  ————  > 0 
      20         100 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       20 

      The right denominator is :       100 

      Least Common Multiple:
      100 

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 = 5

   Right_M = L.C.M / R_Deno = 1

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.      (20b-199) • 5
   ——————————————————  =   —————————————
         L.C.M                  100     

   R. Mult. • R. Num.      -829
   ——————————————————  =   ————
         L.C.M             100 

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (20b-199) • 5 - (-829)     100b - 166
 ——————————————————————  =  ——————————
          100                  100    

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   100b - 166  =   2 • (50b - 83) 

Equation at the end of step  5  :

  2 • (50b - 83)
  ——————————————  > 0 
       100      

Step  6  :

 6.1    Multiply both sides by  100 

 6.2    Divide both sides by  2 

 6.3    Divide both sides by  50  

      b-(83/50)  > 0

Solve Basic Inequality :

 6.4      Add  83/50  to both sides

             b > 83/50

Inequality Plot :

 6.5      Inequality plot for

         X  - 1.660  >  0

  
 

One solution was found :