Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "45.1" was replaced by "(451/10)". 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 :

                     s-((588/10)-(451/10))<0 

Step by step solution :

Step  1  :

            451
 Simplify   ———
            10 

Equation at the end of step  1  :

        588    451
  s -  (——— -  ———)  < 0 
        10     10 

Step  2  :

            294
 Simplify   ———
             5 

Equation at the end of step  2  :

        294    451
  s -  (——— -  ———)  < 0 
         5     10 

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       10 

      Least Common Multiple:
      10 

Calculating Multipliers :

 3.2    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 = 2

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 3.3      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.      294 • 2
   ——————————————————  =   ———————
         L.C.M               10   

   R. Mult. • R. Num.      451
   ——————————————————  =   ———
         L.C.M             10 

Adding fractions that have a common denominator :

 3.4       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:

 294 • 2 - (451)     137
 ———————————————  =  ———
       10            10 

Equation at the end of step  3  :

       137
  s -  ———  < 0 
       10 

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a fraction from a whole

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

          s     s • 10
     s =  —  =  ——————
          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 :

 4.2       Adding up the two equivalent fractions

 s • 10 - (137)     10s - 137
 ——————————————  =  —————————
       10              10    

Equation at the end of step  4  :

  10s - 137
  —————————  < 0 
     10    

Step  5  :

 5.1    Multiply both sides by  10 

 5.2    Divide both sides by  10  

      s-(137/10)  < 0

Solve Basic Inequality :

 5.3      Add  137/10  to both sides

             s < 137/10

Inequality Plot :

 5.4      Inequality plot for

         s  - 13.700  <  0

  
 

One solution was found :