Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.52" was replaced by "(152/100)". 4 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 :

           (46/10)*s-(32/10)-((25/10)-(152/100))<0 

Step by step solution :

Step  1  :

            38
 Simplify   ——
            25

Equation at the end of step  1  :

    46    32   25 38
  ((——•s)-——)-(——-——)  < 0 
    10    10   10 25

Step  2  :

            5
 Simplify   —
            2

Equation at the end of step  2  :

    46    32   5 38
  ((——•s)-——)-(—-——)  < 0 
    10    10   2 25

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       25 

      Least Common Multiple:
      50 

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 = 25

   Right_M = L.C.M / R_Deno = 2

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.      5 • 25
   ——————————————————  =   ——————
         L.C.M               50  

   R. Mult. • R. Num.      38 • 2
   ——————————————————  =   ——————
         L.C.M               50  

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:

 5 • 25 - (38 • 2)     49
 —————————————————  =  ——
        50             50

Equation at the end of step  3  :

    46         32     49
  ((—— • s) -  ——) -  ——  < 0 
    10         10     50

Step  4  :

            16
 Simplify   ——
            5 

Equation at the end of step  4  :

    46         16     49
  ((—— • s) -  ——) -  ——  < 0 
    10         5      50

Step  5  :

            23
 Simplify   ——
            5 

Equation at the end of step  5  :

    23         16     49
  ((—— • s) -  ——) -  ——  < 0 
    5          5      50

Step  6  :

Adding fractions which have a common denominator :

 6.1       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 23s - (16)     23s - 16
 ——————————  =  ————————
     5             5    

Equation at the end of step  6  :

  (23s - 16)    49
  —————————— -  ——  < 0 
      5         50

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       50 

      Least Common Multiple:
      50 

Calculating Multipliers :

 7.2    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 = 10

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 7.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      (23s-16) • 10
   ——————————————————  =   —————————————
         L.C.M                  50      

   R. Mult. • R. Num.      49
   ——————————————————  =   ——
         L.C.M             50

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions

 (23s-16) • 10 - (49)     230s - 209
 ————————————————————  =  ——————————
          50                  50    

Equation at the end of step  7  :

  230s - 209
  ——————————  < 0 
      50    

Step  8  :

 8.1    Multiply both sides by  50 

 8.2    Divide both sides by  230  

      s-(209/230)  < 0

Solve Basic Inequality :

 8.3      Add  209/230  to both sides

             s < 209/230

Inequality Plot :

 8.4      Inequality plot for

         4.600 s  - 4.180  <  0

  
 

One solution was found :