Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "27.5" was replaced by "(275/10)". 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 :

                350*x+(25/10)-(225*x+(275/10))>0 

Step by step solution :

Step  1  :

            55
 Simplify   ——
            2 

Equation at the end of step  1  :

           25              55
  (350x +  ——) -  (225x +  ——)  > 0 
           10              2 

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a fraction to a whole

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

             225x     225x • 2
     225x =  ————  =  ————————
              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 :

 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:

 225x • 2 + 55     450x + 55
 —————————————  =  —————————
       2               2    

Equation at the end of step  2  :

           25     (450x + 55)
  (350x +  ——) -  ———————————  > 0 
           10          2     

Step  3  :

            5
 Simplify   —
            2

Equation at the end of step  3  :

           5     (450x + 55)
  (350x +  —) -  ———————————  > 0 
           2          2     

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a fraction to a whole

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

             350x     350x • 2
     350x =  ————  =  ————————
              1          2    

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 350x • 2 + 5     700x + 5
 ————————————  =  ————————
      2              2    

Equation at the end of step  4  :

  (700x + 5)    (450x + 55)
  —————————— -  ———————————  > 0 
      2              2     

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   700x + 5  =   5 • (140x + 1) 

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   450x + 55  =   5 • (90x + 11) 

Adding fractions which have a common denominator :

 7.2       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:

 5 • (140x+1) - (5 • (90x+11))     250x - 50
 —————————————————————————————  =  —————————
               2                       2    

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   250x - 50  =   50 • (5x - 1) 

Equation at the end of step  8  :

  50 • (5x - 1)
  —————————————  > 0 
        2      

Step  9  :

 9.1    Multiply both sides by  2 

 9.2    Divide both sides by  50 

 9.3    Divide both sides by  5  

      x-(1/5)  > 0

Solve Basic Inequality :

 9.4      Add  1/5  to both sides

             x > 1/5

Inequality Plot :

 9.5      Inequality plot for

         125.000 X  - 25.000  >  0

  
 

One solution was found :