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 :

                     8/5-(s+12/5)>0 

Step by step solution :

Step  1  :

            12
 Simplify   ——
            5 

Equation at the end of step  1  :

  8          12
  — -  (s +  ——)  > 0 
  5          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 :

          s     s • 5
     s =  —  =  —————
          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:

 s • 5 + 12     5s + 12
 ——————————  =  ———————
     5             5   

Equation at the end of step  2  :

  8    (5s + 12)
  — -  —————————  > 0 
  5        5    

Step  3  :

            8
 Simplify   —
            5

Equation at the end of step  3  :

  8    (5s + 12)
  — -  —————————  > 0 
  5        5    

Step  4  :

Adding fractions which have a common denominator :

 4.1       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:

 8 - ((5s+12))     -5s - 4
 —————————————  =  ———————
       5              5   

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   -5s - 4  =   -1 • (5s + 4) 

Equation at the end of step  5  :

  -5s - 4
  ———————  > 0 
     5   

Step  6  :

 6.1    Multiply both sides by  5 

 6.2    Multiply both sides by (-1)

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

      5s+4  < 0

 6.3    Divide both sides by  5  

      s+(4/5)  < 0

Solve Basic Inequality :

 6.4      Subtract  4/5  from both sides

            s < -4/5

Inequality Plot :

 6.5      Inequality plot for

         -s  - 0.800  >  0

  
 

One solution was found :