Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.2" was replaced by "(42/10)". 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 :

                     (72/10)-(x+(42/10))<0 

Step by step solution :

Step  1  :

            21
 Simplify   ——
            5 

Equation at the end of step  1  :

  72          21
  —— -  (x +  ——)  < 0 
  10          5 

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a fraction to a whole

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

          x     x • 5
     x =  —  =  —————
          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 :

 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:

 x • 5 + 21     5x + 21
 ——————————  =  ———————
     5             5   

Equation at the end of step  2  :

  72    (5x + 21)
  —— -  —————————  < 0 
  10        5    

Step  3  :

            36
 Simplify   ——
            5 

Equation at the end of step  3  :

  36    (5x + 21)
  —— -  —————————  < 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:

 36 - ((5x+21))     15 - 5x
 ——————————————  =  ———————
       5               5   

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   15 - 5x  =   -5 • (x - 3) 

Equation at the end of step  5  :

  3 - x  < 0 

Step  6  :

 6.1    Multiply both sides by (-1)

Flip the inequality sign since you are multiplying by a negative number

      x-3  > 0

Solve Basic Inequality :

 6.2      Add  3  to both sides

             x > 3

Inequality Plot :

 6.3      Inequality plot for

         -x  + 3.000  <  0

  
 

One solution was found :