Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "5.24" was replaced by "(524/100)". 2 more similar replacement(s)

Rearrange:

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

                     b-(27/10)-((524/100))≥0 

Step by step solution :

Step  1  :

            131
 Simplify   ———
            25 

Equation at the end of step  1  :

        27     131
  (b -  ——) -  ———  ≥ 0 
        10     25 

Step  2  :

            27
 Simplify   ——
            10

Equation at the end of step  2  :

        27     131
  (b -  ——) -  ———  ≥ 0 
        10     25 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  10  as the denominator :

          b     b • 10
     b =  —  =  ——————
          1       10  

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 • 10 - (27)     10b - 27
 —————————————  =  ————————
      10              10   

Equation at the end of step  3  :

  (10b - 27)    131
  —————————— -  ———  ≥ 0 
      10        25 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       25 

      Least Common Multiple:
      50 

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 = 2

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.      (10b-27) • 5
   ——————————————————  =   ————————————
         L.C.M                  50     

   R. Mult. • R. Num.      131 • 2
   ——————————————————  =   ———————
         L.C.M               50   

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (10b-27) • 5 - (131 • 2)     50b - 397
 ————————————————————————  =  —————————
            50                   50    

Equation at the end of step  4  :

  50b - 397
  —————————  ≥ 0 
     50    

Step  5  :

 5.1    Multiply both sides by  50 

 5.2    Divide both sides by  50  

      b-(397/50)  ≥ 0

Solve Basic Inequality :

 5.3      Add  397/50  to both sides

             b ≥ 397/50

Inequality Plot :

 5.4      Inequality plot for

         b  - 7.940  ≥  0

  
 

One solution was found :