Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "9.04" was replaced by "(904/100)". 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 :

                (113/100)*q-((904/100))≥0 

Step by step solution :

Step  1  :

            226
 Simplify   ———
            25 

Equation at the end of step  1  :

   113         226
  (——— • q) -  ———  ≥ 0 
   100         25 

Step  2  :

            113
 Simplify   ———
            100

Equation at the end of step  2  :

   113         226
  (——— • q) -  ———  ≥ 0 
   100         25 

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       100 

      The right denominator is :       25 

      Least Common Multiple:
      100 

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 = 1

   Right_M = L.C.M / R_Deno = 4

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.      113q
   ——————————————————  =   ————
         L.C.M             100 

   R. Mult. • R. Num.      226 • 4
   ——————————————————  =   ———————
         L.C.M               100  

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:

 113q - (226 • 4)     113q - 904
 ————————————————  =  ——————————
       100               100    

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   113q - 904  =   113 • (q - 8) 

Equation at the end of step  4  :

  113 • (q - 8)
  —————————————  ≥ 0 
       100     

Step  5  :

 5.1    Multiply both sides by  100 

 5.2    Divide both sides by  113 

Solve Basic Inequality :

 5.3      Add  8  to both sides

             q ≥ 8

Inequality Plot :

 5.4      Inequality plot for

         1.130 X  - 9.040  ≥  0

  
 

One solution was found :