Solution - Adding, subtracting and finding the least common multiple

Rearrange:

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

                     3/4*(x+4)-3/2-(3)≥0 

Step by step solution :

Step  1  :

            3
 Simplify   —
            2

Equation at the end of step  1  :

    3               3     
  ((— • (x + 4)) -  —) -  3  ≥ 0 
    4               2     

Step  2  :

            3
 Simplify   —
            4

Equation at the end of step  2  :

    3               3     
  ((— • (x + 4)) -  —) -  3  ≥ 0 
    4               2     

Step  3  :

Equation at the end of step  3  :

   3 • (x + 4)    3     
  (——————————— -  —) -  3  ≥ 0 
        4         2     

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       2 

      Least Common Multiple:
      4 

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 • (x+4)
   ——————————————————  =   —————————
         L.C.M                 4    

   R. Mult. • R. Num.      3 • 2
   ——————————————————  =   —————
         L.C.M               4  

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

Equation at the end of step  4  :

  (3x + 6)    
  ———————— -  3  ≥ 0 
     4        

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a whole from a fraction

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

         3     3 • 4
    3 =  —  =  —————
         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

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   3x + 6  =   3 • (x + 2) 

Adding fractions that have a common denominator :

 6.2       Adding up the two equivalent fractions

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

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   3x - 6  =   3 • (x - 2) 

Equation at the end of step  7  :

  3 • (x - 2)
  ———————————  ≥ 0 
       4     

Step  8  :

 8.1    Multiply both sides by  4 

 8.2    Divide both sides by  3 

Solve Basic Inequality :

 8.3      Add  2  to both sides

             x ≥ 2

Inequality Plot :

 8.4      Inequality plot for

         0.750 X  - 1.500  ≥  0

  
 

One solution was found :