Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.5" was replaced by "(45/10)".

Rearrange:

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

                     -(45/10)-(m/6)>0 

Step by step solution :

Step  1  :

            m
 Simplify   —
            6

Equation at the end of step  1  :

        45     m
  (0 -  ——) -  —  > 0 
        10     6

Step  2  :

            9
 Simplify   —
            2

Equation at the end of step  2  :

        9     m
  (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.      -9 • 3
   ——————————————————  =   ——————
         L.C.M               6   

   R. Mult. • R. Num.      m
   ——————————————————  =   —
         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:

 -9 • 3 - (m)     -m - 27
 ————————————  =  ———————
      6              6   

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   -m - 27  =   -1 • (m + 27) 

Equation at the end of step  4  :

  -m - 27
  ———————  > 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

      m+27  < 0

Solve Basic Inequality :

 5.3      Subtract  27  from both sides

            m < -27

Inequality Plot :

 5.4      Inequality plot for

         -0.167 m  - 4.500  >  0

  
 

One solution was found :