Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.48" was replaced by "(448/100)". 2 more similar replacement(s)

Rearrange:

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

                (1533/100)-((448/100)-w)≤0 

Step by step solution :

Step  1  :

            112
 Simplify   ———
            25 

Equation at the end of step  1  :

  1533     112    
  ———— -  (——— -  w)  ≤ 0 
  100      25     

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  25  as the denominator :

         w     w • 25
    w =  —  =  ——————
         1       25  

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 :

 2.2       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:

 112 - (w • 25)     112 - 25w
 ——————————————  =  —————————
       25              25    

Equation at the end of step  2  :

  1533    (112 - 25w)
  ———— -  ———————————  ≤ 0 
  100         25     

Step  3  :

            1533
 Simplify   ————
            100 

Equation at the end of step  3  :

  1533    (112 - 25w)
  ———— -  ———————————  ≤ 0 
  100         25     

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       100 

      The right denominator is :       25 

      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 = 1

   Right_M = L.C.M / R_Deno = 4

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.      1533
   ——————————————————  =   ————
         L.C.M             100 

   R. Mult. • R. Num.      (112-25w) • 4
   ——————————————————  =   —————————————
         L.C.M                  100     

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 1533 - ((112-25w) • 4)     100w + 1085
 ——————————————————————  =  ———————————
          100                   100    

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   100w + 1085  =   5 • (20w + 217) 

Equation at the end of step  5  :

  5 • (20w + 217)
  ———————————————  ≤ 0 
        100      

Step  6  :

 6.1    Multiply both sides by  100 

 6.2    Divide both sides by  5 

 6.3    Divide both sides by  20  

      w+(217/20)  ≤ 0

Solve Basic Inequality :

 6.4      Subtract  217/20  from both sides

            w ≤ -217/20

Inequality Plot :

 6.5      Inequality plot for

         X  + 10.850  ≤  0

  
 

One solution was found :