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 :

                     3+5/2*x-(2*x-13/2)>0 

Step by step solution :

Step  1  :

            13
 Simplify   ——
            2 

Equation at the end of step  1  :

         5                 13
  (3 +  (— • x)) -  (2x -  ——)  > 0 
         2                 2 

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

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

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

 2x • 2 - (13)     4x - 13
 —————————————  =  ———————
       2              2   

Equation at the end of step  2  :

         5          (4x - 13)
  (3 +  (— • x)) -  —————————  > 0 
         2              2    

Step  3  :

            5
 Simplify   —
            2

Equation at the end of step  3  :

         5          (4x - 13)
  (3 +  (— • x)) -  —————————  > 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 :

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

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 3 • 2 + 5x     5x + 6
 ——————————  =  ——————
     2            2   

Equation at the end of step  4  :

  (5x + 6)    (4x - 13)
  ———————— -  —————————  > 0 
     2            2    

Step  5  :

Adding fractions which have a common denominator :

 5.1       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:

 (5x+6) - ((4x-13))     x + 19
 ——————————————————  =  ——————
         2                2   

Equation at the end of step  5  :

  x + 19
  ——————  > 0 
    2   

Step  6  :

 6.1    Multiply both sides by  2 

Solve Basic Inequality :

 6.2      Subtract  19  from both sides

            x > -19

Inequality Plot :

 6.3      Inequality plot for

         0.500 x  + 9.500  >  0

  
 

One solution was found :