Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "45.4" was replaced by "(454/10)". 2 more similar replacement(s)

Rearrange:

Rearrange the equation by subtracting what is to the right of the less equal sign from both sides of the inequality :

                x+(182/10)+(454/10)-(100)≤0 

Step by step solution :

Step  1  :

            227
 Simplify   ———
             5 

Equation at the end of step  1  :

         182     227     
  ((x +  ———) +  ———) -  100  ≤ 0 
         10       5      

Step  2  :

            91
 Simplify   ——
            5 

Equation at the end of step  2  :

         91     227     
  ((x +  ——) +  ———) -  100  ≤ 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 :

          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 :

 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:

 x • 5 + 91     5x + 91
 ——————————  =  ———————
     5             5   

Equation at the end of step  3  :

   (5x + 91)    227     
  (————————— +  ———) -  100  ≤ 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:

 (5x+91) + 227     5x + 318
 —————————————  =  ————————
       5              5    

Equation at the end of step  4  :

  (5x + 318)    
  —————————— -  100  ≤ 0 
      5         

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a whole from a fraction

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

           100     100 • 5
    100 =  ———  =  ———————
            1         5   

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 (5x+318) - (100 • 5)     5x - 182
 ————————————————————  =  ————————
          5                  5    

Equation at the end of step  5  :

  5x - 182
  ————————  ≤ 0 
     5    

Step  6  :

 6.1    Multiply both sides by  5 

 6.2    Divide both sides by  5  

      x-(182/5)  ≤ 0

Solve Basic Inequality :

 6.3      Add  182/5  to both sides

             x ≤ 182/5

Inequality Plot :

 6.4      Inequality plot for

         x  - 36.400  ≤  0

  
 

One solution was found :