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 :

                     1/6*(3-2*x)-(1/3*x)<0 

Step by step solution :

Step  1  :

            1
 Simplify   —
            3

Equation at the end of step  1  :

   1                 1
  (— • (3 - 2x)) -  (— • x)  < 0 
   6                 3

Step  2  :

            1
 Simplify   —
            6

Equation at the end of step  2  :

   1                x
  (— • (3 - 2x)) -  —  < 0 
   6                3

Step  3  :

Equation at the end of step  3  :

  (3 - 2x)    x
  ———————— -  —  < 0 
     6        3

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       6 

      The right denominator is :       3 

      Least Common Multiple:
      6 

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 = 2

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.      (3-2x)
   ——————————————————  =   ——————
         L.C.M               6   

   R. Mult. • R. Num.      x • 2
   ——————————————————  =   —————
         L.C.M               6  

Adding fractions that have a common denominator :

 4.4       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:

 (3-2x) - (x • 2)     3 - 4x
 ————————————————  =  ——————
        6               6   

Equation at the end of step  4  :

  3 - 4x
  ——————  < 0 
    6   

Step  5  :

 5.1    Multiply both sides by  6 

 5.2    Multiply both sides by (-1)

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

      4x-3  > 0

 5.3    Divide both sides by  4  

      x-(3/4)  > 0

Solve Basic Inequality :

 5.4      Add  3/4  to both sides

             x > 3/4

Inequality Plot :

 5.5      Inequality plot for

         -0.667 x  + 0.500  <  0

  
 

One solution was found :