Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.3" was replaced by "(43/10)". 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 :

                     (113/10)-(b/(43/10))>0 

Step by step solution :

Step  1  :

            43
 Simplify   ——
            10

Equation at the end of step  1  :

  113    43
  ——— -  ——  > 0 
  10     10

Step  2  :

                43
 Divide  b  by  ——
                10

Equation at the end of step  2  :

  113    10b
  ——— -  ———  > 0 
  10     43 

Step  3  :

            113
 Simplify   ———
            10 

Equation at the end of step  3  :

  113    10b
  ——— -  ———  > 0 
  10     43 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       43 

      Least Common Multiple:
      430 

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 = 43

   Right_M = L.C.M / R_Deno = 10

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.      113 • 43
   ——————————————————  =   ————————
         L.C.M               430   

   R. Mult. • R. Num.      10b • 10
   ——————————————————  =   ————————
         L.C.M               430   

Adding fractions that have a common denominator :

 4.4       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:

 113 • 43 - (10b • 10)     4859 - 100b
 —————————————————————  =  ———————————
          430                  430    

Equation at the end of step  4  :

  4859 - 100b
  ———————————  > 0 
      430    

Step  5  :

 5.1    Multiply both sides by  430 

 5.2    Multiply both sides by (-1)

Flip the inequality sign since you are multiplying by a negative number

      100b-4859  < 0

 5.3    Divide both sides by  100  

      b-(4859/100)  < 0

Solve Basic Inequality :

 5.4      Add  4859/100  to both sides

             b < 4859/100

Inequality Plot :

 5.5      Inequality plot for

         -0.233 b  + 11.300  >  0

  
 

One solution was found :