Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.74" was replaced by "(74/100)". 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 :

                10-((499/100)+(74/100)*x)≥0 

Step by step solution :

Step  1  :

            37
 Simplify   ——
            50

Equation at the end of step  1  :

         499     37
  10 -  (——— +  (—— • x))  ≥ 0 
         100     50

Step  2  :

            499
 Simplify   ———
            100

Equation at the end of step  2  :

         499    37x
  10 -  (——— +  ———)  ≥ 0 
         100    50 

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       100 

      The right denominator is :       50 

      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 = 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.      499
   ——————————————————  =   ———
         L.C.M             100

   R. Mult. • R. Num.      37x • 2
   ——————————————————  =   ———————
         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:

 499 + 37x • 2     74x + 499
 —————————————  =  —————————
      100             100   

Equation at the end of step  3  :

        (74x + 499)
  10 -  ———————————  ≥ 0 
            100    

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a fraction from a whole

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

           10     10 • 100
     10 =  ——  =  ————————
           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 :

 4.2       Adding up the two equivalent fractions

 10 • 100 - ((74x+499))     501 - 74x
 ——————————————————————  =  —————————
          100                  100   

Equation at the end of step  4  :

  501 - 74x
  —————————  ≥ 0 
     100   

Step  5  :

 5.1    Multiply both sides by  100 

 5.2    Multiply both sides by (-1)

Flip the inequality sign since you are multiplying by a negative number

      74x-501  ≤ 0

 5.3    Divide both sides by  74  

      x-(501/74)  ≤ 0

Solve Basic Inequality :

 5.4      Add  501/74  to both sides

             x ≤ 501/74

Inequality Plot :

 5.5      Inequality plot for

         -0.740 x  + 5.010  ≥  0

  
 

One solution was found :