Solution - Adding, subtracting and finding the least common multiple

Rearrange:

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

                     x*1/3-(5/6)<0 

Step by step solution :

Step  1  :

            5
 Simplify   —
            6

Equation at the end of step  1  :

       1     5
  (x • —) -  —  < 0 
       3     6

Step  2  :

            1
 Simplify   —
            3

Equation at the end of step  2  :

       1     5
  (x • —) -  —  < 0 
       3     6

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       3 

      The right denominator is :       6 

      Least Common Multiple:
      6 

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 = 2

   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.      x • 2
   ——————————————————  =   —————
         L.C.M               6  

   R. Mult. • R. Num.      5
   ——————————————————  =   —
         L.C.M             6

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:

 x • 2 - (5)     2x - 5
 ———————————  =  ——————
      6            6   

Equation at the end of step  3  :

  2x - 5
  ——————  < 0 
    6   

Step  4  :

 4.1    Multiply both sides by  6 

 4.2    Divide both sides by  2  

      x-(5/2)  < 0

Solve Basic Inequality :

 4.3      Add  5/2  to both sides

             x < 5/2

Inequality Plot :

 4.4      Inequality plot for

         0.333 x  - 0.833  <  0

  
 

One solution was found :