Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3.5" was replaced by "(35/10)". 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 :

                2*x+4-(11*x-(125/10)-(35/10)*x)>0 

Step by step solution :

Step  1  :

            7
 Simplify   —
            2

Equation at the end of step  1  :

                       125      7
  (2x + 4) -  ((11x -  ———) -  (— • x))  > 0 
                       10       2

Step  2  :

            25
 Simplify   ——
            2 

Equation at the end of step  2  :

                       25     7x
  (2x + 4) -  ((11x -  ——) -  ——)  > 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 :

            11x     11x • 2
     11x =  ———  =  ———————
             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:

 11x • 2 - (25)     22x - 25
 ——————————————  =  ————————
       2               2    

Equation at the end of step  3  :

               (22x - 25)    7x
  (2x + 4) -  (—————————— -  ——)  > 0 
                   2         2 

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:

 (22x-25) - (7x)     15x - 25
 ———————————————  =  ————————
        2               2    

Equation at the end of step  4  :

              (15x - 25)
  (2x + 4) -  ——————————  > 0 
                  2     

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a fraction from a whole

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

               2x + 4     (2x + 4) • 2
     2x + 4 =  ——————  =  ————————————
                 1             2      

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   2x + 4  =   2 • (x + 2) 

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   15x - 25  =   5 • (3x - 5) 

Adding fractions that have a common denominator :

 7.2       Adding up the two equivalent fractions

 2 • (x+2) • 2 - (5 • (3x-5))     33 - 11x
 ————————————————————————————  =  ————————
              2                      2    

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   33 - 11x  =   -11 • (x - 3) 

Equation at the end of step  8  :

  -11 • (x - 3)
  —————————————  > 0 
        2      

Step  9  :

 9.1    Multiply both sides by  2 

 9.2    Divide both sides by  -11 

Remember to flip the inequality sign:

Solve Basic Inequality :

 9.3      Add  3  to both sides

             x < 3

Inequality Plot :

 9.4      Inequality plot for

         -5.500 X  + 16.500  <  0

  
 

One solution was found :