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 :

                     -r/2-(-5/6)<0 

Step by step solution :

Step  1  :

            5
 Simplify   —
            6

Equation at the end of step  1  :

        r           5
  (0 -  —) -  (0 -  —)  < 0 
        2           6

Step  2  :

            r
 Simplify   —
            2

Equation at the end of step  2  :

        r     -5
  (0 -  —) -  ——  < 0 
        2     6 

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       6 

      Least Common Multiple:
      6 

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 = 3

   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.      -r • 3
   ——————————————————  =   ——————
         L.C.M               6   

   R. Mult. • R. Num.      -5
   ——————————————————  =   ——
         L.C.M             6 

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:

 -r • 3 - (-5)     5 - 3r
 —————————————  =  ——————
       6             6   

Equation at the end of step  3  :

  5 - 3r
  ——————  < 0 
    6   

Step  4  :

 4.1    Multiply both sides by  6 

 4.2    Multiply both sides by (-1)

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

      3r-5  > 0

 4.3    Divide both sides by  3  

      r-(5/3)  > 0

Solve Basic Inequality :

 4.4      Add  5/3  to both sides

             r > 5/3

Inequality Plot :

 4.5      Inequality plot for

         -0.500 r  + 0.833  <  0

  
 

One solution was found :