Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "7.7" was replaced by "(77/10)". 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 :

                     (23/10)+x-((77/10))<0 

Step by step solution :

Step  1  :

            77
 Simplify   ——
            10

Equation at the end of step  1  :

   23          77
  (—— +  x) -  ——  < 0 
   10          10

Step  2  :

            23
 Simplify   ——
            10

Equation at the end of step  2  :

   23          77
  (—— +  x) -  ——  < 0 
   10          10

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  10  as the denominator :

         x     x • 10
    x =  —  =  ——————
         1       10  

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:

 23 + x • 10     10x + 23
 ———————————  =  ————————
     10             10   

Equation at the end of step  3  :

  (10x + 23)    77
  —————————— -  ——  < 0 
      10        10

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:

 (10x+23) - (77)     10x - 54
 ———————————————  =  ————————
       10               10   

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   10x - 54  =   2 • (5x - 27) 

Equation at the end of step  5  :

  2 • (5x - 27)
  —————————————  < 0 
       10      

Step  6  :

 6.1    Multiply both sides by  10 

 6.2    Divide both sides by  2 

 6.3    Divide both sides by  5  

      x-(27/5)  < 0

Solve Basic Inequality :

 6.4      Add  27/5  to both sides

             x < 27/5

Inequality Plot :

 6.5      Inequality plot for

         X  - 5.400  <  0

  
 

One solution was found :