Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "19.68" was replaced by "(1968/100)". 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 :

                d-(1426/100)-(-(1968/100))≤0 

Step by step solution :

Step  1  :

            492
 Simplify   ———
            25 

Equation at the end of step  1  :

        1426           492
  (d -  ————) -  (0 -  ———)  ≤ 0 
        100            25 

Step  2  :

            713
 Simplify   ———
            50 

Equation at the end of step  2  :

        713     -492
  (d -  ———) -  ————  ≤ 0 
        50       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  50  as the denominator :

          d     d • 50
     d =  —  =  ——————
          1       50  

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:

 d • 50 - (713)     50d - 713
 ——————————————  =  —————————
       50              50    

Equation at the end of step  3  :

  (50d - 713)    -492
  ——————————— -  ————  ≤ 0 
      50          25 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       50 

      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 = 1

   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.      (50d-713)
   ——————————————————  =   —————————
         L.C.M                50    

   R. Mult. • R. Num.      -492 • 2
   ——————————————————  =   ————————
         L.C.M                50   

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (50d-713) - (-492 • 2)     50d + 271
 ——————————————————————  =  —————————
           50                  50    

Equation at the end of step  4  :

  50d + 271
  —————————  ≤ 0 
     50    

Step  5  :

 5.1    Multiply both sides by  50 

 5.2    Divide both sides by  50  

      d+(271/50)  ≤ 0

Solve Basic Inequality :

 5.3      Subtract  271/50  from both sides

            d ≤ -271/50

Inequality Plot :

 5.4      Inequality plot for

         d  + 5.420  ≤  0

  
 

One solution was found :