Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "14.2" was replaced by "(142/10)". 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 :

                5/5*n-(98/10)-((142/10))<0 

Step by step solution :

Step  1  :

            71
 Simplify   ——
            5 

Equation at the end of step  1  :

    5         98     71
  ((— • n) -  ——) -  ——  < 0 
    5         10     5 

Step  2  :

            49
 Simplify   ——
            5 

Equation at the end of step  2  :

    5         49     71
  ((— • n) -  ——) -  ——  < 0 
    5         5      5 

Step  3  :

            1
 Simplify   —
            1

Equation at the end of step  3  :

              49     71
  ((1 • n) -  ——) -  ——  < 0 
              5      5 

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a fraction from a whole

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

          n     n • 5
     n =  —  =  —————
          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 :

 4.2       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:

 n • 5 - (49)     5n - 49
 ————————————  =  ———————
      5              5   

Equation at the end of step  4  :

  (5n - 49)    71
  ————————— -  ——  < 0 
      5        5 

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:

 (5n-49) - (71)     5n - 120
 ——————————————  =  ————————
       5               5    

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   5n - 120  =   5 • (n - 24) 

Equation at the end of step  6  :

  n - 24  < 0 

Step  7  :

Solve Basic Inequality :

 7.1      Add  24  to both sides

             n < 24

Inequality Plot :

 7.2      Inequality plot for

         n  - 24.000  <  0

  
 

One solution was found :