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+3)/4-2-((x-1)/3)>0 

Step by step solution :

Step  1  :

            x - 1
 Simplify   —————
              3  

Equation at the end of step  1  :

   (x + 3)          (x - 1)
  (——————— -  2) -  ———————  > 0 
      4                3   

Step  2  :

            x + 3
 Simplify   —————
              4  

Equation at the end of step  2  :

   (x + 3)          (x - 1)
  (——————— -  2) -  ———————  > 0 
      4                3   

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  4  as the denominator :

         2     2 • 4
    2 =  —  =  —————
         1       4  

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 :

 3.2       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+3) - (2 • 4)     x - 5
 ———————————————  =  —————
        4              4  

Equation at the end of step  3  :

  (x - 5)    (x - 1)
  ——————— -  ———————  > 0 
     4          3   

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       3 

      Least Common Multiple:
      12 

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 = 3

   Right_M = L.C.M / R_Deno = 4

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.      (x-5) • 3
   ——————————————————  =   —————————
         L.C.M                12    

   R. Mult. • R. Num.      (x-1) • 4
   ——————————————————  =   —————————
         L.C.M                12    

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (x-5) • 3 - ((x-1) • 4)     -x - 11
 ———————————————————————  =  ———————
           12                  12   

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   -x - 11  =   -1 • (x + 11) 

Equation at the end of step  5  :

  -x - 11
  ———————  > 0 
    12   

Step  6  :

 6.1    Multiply both sides by  12 

 6.2    Multiply both sides by (-1)

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

      x+11  < 0

Solve Basic Inequality :

 6.3      Subtract  11  from both sides

            x < -11

Inequality Plot :

 6.4      Inequality plot for

         -0.083 x  - 0.917  >  0

  
 

One solution was found :