Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "25.5" was replaced by "(255/10)". 2 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 :

                3*x-(15/10)-((255/10))<0 

Step by step solution :

Step  1  :

            51
 Simplify   ——
            2 

Equation at the end of step  1  :

         15     51
  (3x -  ——) -  ——  < 0 
         10     2 

Step  2  :

            3
 Simplify   —
            2

Equation at the end of step  2  :

         3     51
  (3x -  —) -  ——  < 0 
         2     2 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

           3x     3x • 2
     3x =  ——  =  ——————
           1        2   

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:

 3x • 2 - (3)     6x - 3
 ————————————  =  ——————
      2             2   

Equation at the end of step  3  :

  (6x - 3)    51
  ———————— -  ——  < 0 
     2        2 

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   6x - 3  =   3 • (2x - 1) 

Adding fractions which have a common denominator :

 5.2       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:

 3 • (2x-1) - (51)     6x - 54
 —————————————————  =  ———————
         2                2   

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   6x - 54  =   6 • (x - 9) 

Equation at the end of step  6  :

  6 • (x - 9)
  ———————————  < 0 
       2     

Step  7  :

 7.1    Multiply both sides by  2 

 7.2    Divide both sides by  6 

Solve Basic Inequality :

 7.3      Add  9  to both sides

             x < 9

Inequality Plot :

 7.4      Inequality plot for

         3.000 X  - 27.000  <  0

  
 

One solution was found :