Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "8.6" was replaced by "(86/10)". 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 :

                (72/10)-((9/10)*(n+(86/10)))>0 

Step by step solution :

Step  1  :

            43
 Simplify   ——
            5 

Equation at the end of step  1  :

  72      9         43
  —— -  (—— • (n +  ——))  > 0 
  10     10         5 

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  5  as the denominator :

          n     n • 5
     n =  —  =  —————
          1       5  

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 :

 2.2       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:

 n • 5 + 43     5n + 43
 ——————————  =  ———————
     5             5   

Equation at the end of step  2  :

  72      9   (5n + 43)
  —— -  (—— • —————————)  > 0 
  10     10       5    

Step  3  :

             9
 Simplify   ——
            10

Equation at the end of step  3  :

  72      9   (5n + 43)
  —— -  (—— • —————————)  > 0 
  10     10       5    

Step  4  :

Equation at the end of step  4  :

  72    9 • (5n + 43)
  —— -  —————————————  > 0 
  10         50      

Step  5  :

            36
 Simplify   ——
            5 

Equation at the end of step  5  :

  36    9 • (5n + 43)
  —— -  —————————————  > 0 
  5          50      

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       50 

      Least Common Multiple:
      50 

Calculating Multipliers :

 6.2    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 = 10

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 6.3      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.      36 • 10
   ——————————————————  =   ———————
         L.C.M               50   

   R. Mult. • R. Num.      9 • (5n+43)
   ——————————————————  =   ———————————
         L.C.M                 50     

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 36 • 10 - (9 • (5n+43))     -45n - 27
 ———————————————————————  =  —————————
           50                   50    

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   -45n - 27  =   -9 • (5n + 3) 

Equation at the end of step  7  :

  -9 • (5n + 3)
  —————————————  > 0 
       50      

Step  8  :

 8.1    Multiply both sides by  50 

 8.2    Divide both sides by  -9 

Remember to flip the inequality sign:

 8.3    Divide both sides by  5  

      n+(3/5)  < 0

Solve Basic Inequality :

 8.4      Subtract  3/5  from both sides

            n < -3/5

Inequality Plot :

 8.5      Inequality plot for

         -0.900 X  - 0.540  <  0

  
 

One solution was found :