Solution - Adding, subtracting and finding the least common multiple

Rearrange:

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

                     (11*x)/3-(2/9)≤0 

Step by step solution :

Step  1  :

            2
 Simplify   —
            9

Equation at the end of step  1  :

  11x    2
  ——— -  —  ≤ 0 
   3     9

Step  2  :

            11x
 Simplify   ———
             3 

Equation at the end of step  2  :

  11x    2
  ——— -  —  ≤ 0 
   3     9

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       3 

      The right denominator is :       9 

      Least Common Multiple:
      9 

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 = 3

   Right_M = L.C.M / R_Deno = 1

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.      11x • 3
   ——————————————————  =   ———————
         L.C.M                9   

   R. Mult. • R. Num.      2
   ——————————————————  =   —
         L.C.M             9

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:

 11x • 3 - (2)     33x - 2
 —————————————  =  ———————
       9              9   

Equation at the end of step  3  :

  33x - 2
  ———————  ≤ 0 
     9   

Step  4  :

 4.1    Multiply both sides by  9 

 4.2    Divide both sides by  33  

      x-(2/33)  ≤ 0

Solve Basic Inequality :

 4.3      Add  2/33  to both sides

             x ≤ 2/33

Inequality Plot :

 4.4      Inequality plot for

         3.667 x  - 0.222  ≤  0

  
 

One solution was found :