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 :

                     1/2*(x+1)-(1/3*(x+2))>0 

Step by step solution :

Step  1  :

            1
 Simplify   —
            3

Equation at the end of step  1  :

   1                1
  (— • (x + 1)) -  (— • (x + 2))  > 0 
   2                3

Step  2  :

Equation at the end of step  2  :

   1               (x + 2)
  (— • (x + 1)) -  ———————  > 0 
   2                  3   

Step  3  :

            1
 Simplify   —
            2

Equation at the end of step  3  :

   1               (x + 2)
  (— • (x + 1)) -  ———————  > 0 
   2                  3   

Step  4  :

Equation at the end of step  4  :

  (x + 1)    (x + 2)
  ——————— -  ———————  > 0 
     2          3   

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       3 

      Least Common Multiple:
      6 

Calculating Multipliers :

 5.2    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 = 2

Making Equivalent Fractions :

 5.3      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+1) • 3
   ——————————————————  =   —————————
         L.C.M                 6    

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

Adding fractions that have a common denominator :

 5.4       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+1) • 3 - ((x+2) • 2)     x - 1
 ———————————————————————  =  —————
            6                  6  

Equation at the end of step  5  :

  x - 1
  —————  > 0 
    6  

Step  6  :

 6.1    Multiply both sides by  6 

Solve Basic Inequality :

 6.2      Add  1  to both sides

             x > 1

Inequality Plot :

 6.3      Inequality plot for

         0.167 x  - 0.167  >  0

  
 

One solution was found :