Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "22.2" was replaced by "(222/10)". 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 :

                     a+(72/10)-((222/10))<0 

Step by step solution :

Step  1  :

            111
 Simplify   ———
             5 

Equation at the end of step  1  :

        72     111
  (a +  ——) -  ———  < 0 
        10      5 

Step  2  :

            36
 Simplify   ——
            5 

Equation at the end of step  2  :

        36     111
  (a +  ——) -  ———  < 0 
        5       5 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  5  as the denominator :

          a     a • 5
     a =  —  =  —————
          1       5  

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:

 a • 5 + 36     5a + 36
 ——————————  =  ———————
     5             5   

Equation at the end of step  3  :

  (5a + 36)    111
  ————————— -  ———  < 0 
      5         5 

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:

 (5a+36) - (111)     5a - 75
 ———————————————  =  ———————
        5               5   

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   5a - 75  =   5 • (a - 15) 

Equation at the end of step  5  :

  a - 15  < 0 

Step  6  :

Solve Basic Inequality :

 6.1      Add  15  to both sides

             a < 15

Inequality Plot :

 6.2      Inequality plot for

         a  - 15.000  <  0

  
 

One solution was found :