Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.6" was replaced by "(6/10)". 3 more similar replacement(s)

Rearrange:

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

                -(13/10)-((29/10)-(6/10)*n)>0 

Step by step solution :

Step  1  :

            3
 Simplify   —
            5

Equation at the end of step  1  :

     13   29  3
  (0-——)-(——-(—•n))  > 0 
     10   10  5

Step  2  :

            29
 Simplify   ——
            10

Equation at the end of step  2  :

        13      29    3n
  (0 -  ——) -  (—— -  ——)  > 0 
        10      10    5 

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       5 

      Least Common Multiple:
      10 

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 = 1

   Right_M = L.C.M / R_Deno = 2

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.      29
   ——————————————————  =   ——
         L.C.M             10

   R. Mult. • R. Num.      3n • 2
   ——————————————————  =   ——————
         L.C.M               10  

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:

 29 - (3n • 2)     29 - 6n
 —————————————  =  ———————
      10             10   

Equation at the end of step  3  :

        13     (29 - 6n)
  (0 -  ——) -  —————————  > 0 
        10        10    

Step  4  :

            13
 Simplify   ——
            10

Equation at the end of step  4  :

        13     (29 - 6n)
  (0 -  ——) -  —————————  > 0 
        10        10    

Step  5  :

Adding fractions which have a common denominator :

 5.1       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 -13 - ((29-6n))     6n - 42
 ———————————————  =  ———————
       10              10   

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   6n - 42  =   6 • (n - 7) 

Equation at the end of step  6  :

  6 • (n - 7)
  ———————————  > 0 
      10     

Step  7  :

 7.1    Multiply both sides by  10 

 7.2    Divide both sides by  6 

Solve Basic Inequality :

 7.3      Add  7  to both sides

             n > 7

Inequality Plot :

 7.4      Inequality plot for

         0.600 X  - 4.200  >  0

  
 

One solution was found :