Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "8.4" was replaced by "(84/10)". 2 more similar replacement(s)

Rearrange:

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

                     x-(767/100)-((84/10))≥0 

Step by step solution :

Step  1  :

            42
 Simplify   ——
            5 

Equation at the end of step  1  :

        767     42
  (x -  ———) -  ——  ≥ 0 
        100     5 

Step  2  :

            767
 Simplify   ———
            100

Equation at the end of step  2  :

        767     42
  (x -  ———) -  ——  ≥ 0 
        100     5 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  100  as the denominator :

          x     x • 100
     x =  —  =  ———————
          1       100  

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:

 x • 100 - (767)     100x - 767
 ———————————————  =  ——————————
       100              100    

Equation at the end of step  3  :

  (100x - 767)    42
  ———————————— -  ——  ≥ 0 
      100         5 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       100 

      The right denominator is :       5 

      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 = 20

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.      (100x-767)
   ——————————————————  =   ——————————
         L.C.M                100    

   R. Mult. • R. Num.      42 • 20
   ——————————————————  =   ———————
         L.C.M               100  

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (100x-767) - (42 • 20)     100x - 1607
 ——————————————————————  =  ———————————
          100                   100    

Equation at the end of step  4  :

  100x - 1607
  ———————————  ≥ 0 
      100    

Step  5  :

 5.1    Multiply both sides by  100 

 5.2    Divide both sides by  100  

      x-(1607/100)  ≥ 0

Solve Basic Inequality :

 5.3      Add  1607/100  to both sides

             x ≥ 1607/100

Inequality Plot :

 5.4      Inequality plot for

         x  - 16.070  ≥  0

  
 

One solution was found :