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 :

                     1/3*n-4/9*n-(-2)>0 

Step by step solution :

Step  1  :

            4
 Simplify   —
            9

Equation at the end of step  1  :

    1          4          
  ((— • n) -  (— • n)) -  -2  > 0 
    3          9          

Step  2  :

            1
 Simplify   —
            3

Equation at the end of step  2  :

    1         4n     
  ((— • n) -  ——) -  -2  > 0 
    3         9      

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       3 

      The right denominator is :       9 

      Least Common Multiple:
      9 

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.      n • 3
   ——————————————————  =   —————
         L.C.M               9  

   R. Mult. • R. Num.      4n
   ——————————————————  =   ——
         L.C.M             9 

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:

 n • 3 - (4n)     -n
 ————————————  =  ——
      9           9 

Equation at the end of step  3  :

  -n    
  —— -  -2  > 0 
  9     

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  9  as the denominator :

          -2     -2 • 9
    -2 =  ——  =  ——————
          1        9   

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 :

 4.2       Adding up the two equivalent fractions

 -n - (-2 • 9)     18 - n
 —————————————  =  ——————
       9             9   

Equation at the end of step  4  :

  18 - n
  ——————  > 0 
    9   

Step  5  :

 5.1    Multiply both sides by  9 

 5.2    Multiply both sides by (-1)

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

      n-18  < 0

Solve Basic Inequality :

 5.3      Add  18  to both sides

             n < 18

Inequality Plot :

 5.4      Inequality plot for

         -0.111 n  + 2.000  >  0

  
 

One solution was found :