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 :

                     4/3*s-3-(s+2/3-1/3*s)<0 

Step by step solution :

Step  1  :

            1
 Simplify   —
            3

Equation at the end of step  1  :

    4           2   1
  ((—•s)-3)-((s+—)-(—•s))  < 0 
    3           3   3

Step  2  :

            2
 Simplify   —
            3

Equation at the end of step  2  :

    4           2  s
  ((—•s)-3)-((s+—)-—)  < 0 
    3           3  3

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  3  as the denominator :

          s     s • 3
     s =  —  =  —————
          1       3  

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 :

 3.2       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 • 3 + 2     3s + 2
 —————————  =  ——————
     3           3   

Equation at the end of step  3  :

    4                (3s + 2)    s
  ((— • s) -  3) -  (———————— -  —)  < 0 
    3                   3        3

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:

 (3s+2) - (s)     2s + 2
 ————————————  =  ——————
      3             3   

Equation at the end of step  4  :

    4               (2s + 2)
  ((— • s) -  3) -  ————————  < 0 
    3                  3    

Step  5  :

            4
 Simplify   —
            3

Equation at the end of step  5  :

    4               (2s + 2)
  ((— • s) -  3) -  ————————  < 0 
    3                  3    

Step  6  :

Rewriting the whole as an Equivalent Fraction :

 6.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  3  as the denominator :

         3     3 • 3
    3 =  —  =  —————
         1       3  

Adding fractions that have a common denominator :

 6.2       Adding up the two equivalent fractions

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

Equation at the end of step  6  :

  (4s - 9)    (2s + 2)
  ———————— -  ————————  < 0 
     3           3    

Step  7  :

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   2s + 2  =   2 • (s + 1) 

Adding fractions which have a common denominator :

 8.2       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:

 (4s-9) - (2 • (s+1))     2s - 11
 ————————————————————  =  ———————
          3                  3   

Equation at the end of step  8  :

  2s - 11
  ———————  < 0 
     3   

Step  9  :

 9.1    Multiply both sides by  3 

 9.2    Divide both sides by  2  

      s-(11/2)  < 0

Solve Basic Inequality :

 9.3      Add  11/2  to both sides

             s < 11/2

Inequality Plot :

 9.4      Inequality plot for

         0.667 s  - 3.667  <  0

  
 

One solution was found :