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 :

                8*(1/2*x-1/4)-(12-2*x)>0 

Step by step solution :

Step  1  :

            1
 Simplify   —
            4

Equation at the end of step  1  :

         1         1      
  (8 • ((— • x) -  —)) -  (12 - 2x)  > 0 
         2         4      

Step  2  :

            1
 Simplify   —
            2

Equation at the end of step  2  :

         1         1      
  (8 • ((— • x) -  —)) -  (12 - 2x)  > 0 
         2         4      

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       4 

      Least Common Multiple:
      4 

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               4  

   R. Mult. • R. Num.      1
   ——————————————————  =   —
         L.C.M             4

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 - (1)     2x - 1
 ———————————  =  ——————
      4            4   

Equation at the end of step  3  :

       (2x - 1)     
  (8 • ————————) -  (12 - 2x)  > 0 
          4         

Step  4  :

Equation at the end of step  4  :

  2 • (2x - 1) -  (12 - 2x)  > 0 

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   6x - 14  =   2 • (3x - 7) 

Equation at the end of step  6  :

  2 • (3x - 7)  > 0 

Step  7  :

 7.1    Divide both sides by  2 

 7.2    Divide both sides by  3  

      x-(7/3)  > 0

Solve Basic Inequality :

 7.3      Add  7/3  to both sides

             x > 7/3

Inequality Plot :

 7.4      Inequality plot for

         6.000 X  - 14.000  >  0

  
 

One solution was found :