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 :

                     5-3/2*x-(1/3)>0 

Step by step solution :

Step  1  :

            1
 Simplify   —
            3

Equation at the end of step  1  :

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

Step  2  :

            3
 Simplify   —
            2

Equation at the end of step  2  :

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

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

          5     5 • 2
     5 =  —  =  —————
          1       2  

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:

 5 • 2 - (3x)     10 - 3x
 ————————————  =  ———————
      2              2   

Equation at the end of step  3  :

  (10 - 3x)    1
  ————————— -  —  > 0 
      2        3

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       2 

      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 = 3

   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.      (10-3x) • 3
   ——————————————————  =   ———————————
         L.C.M                  6     

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

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (10-3x) • 3 - (2)     28 - 9x
 —————————————————  =  ———————
         6                6   

Equation at the end of step  4  :

  28 - 9x
  ———————  > 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

      9x-28  < 0

 5.3    Divide both sides by  9  

      x-(28/9)  < 0

Solve Basic Inequality :

 5.4      Add  28/9  to both sides

             x < 28/9

Inequality Plot :

 5.5      Inequality plot for

         -1.500 x  + 4.667  >  0

  
 

One solution was found :