Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.7" was replaced by "(27/10)". 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 :

                24-(53/10)*x-((27/10)*x)<0 

Step by step solution :

Step  1  :

            27
 Simplify   ——
            10

Equation at the end of step  1  :

          53           27
  (24 -  (—— • x)) -  (—— • x)  < 0 
          10           10

Step  2  :

            53
 Simplify   ——
            10

Equation at the end of step  2  :

          53          27x
  (24 -  (—— • x)) -  ———  < 0 
          10          10 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

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

           24     24 • 10
     24 =  ——  =  ———————
           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:

 24 • 10 - (53x)     240 - 53x
 ———————————————  =  —————————
       10               10    

Equation at the end of step  3  :

  (240 - 53x)    27x
  ——————————— -  ———  < 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:

 (240-53x) - (27x)     240 - 80x
 —————————————————  =  —————————
        10                10    

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   240 - 80x  =   -80 • (x - 3) 

Equation at the end of step  5  :

  -80 • (x - 3)
  —————————————  < 0 
       10      

Step  6  :

 6.1    Multiply both sides by  10 

 6.2    Divide both sides by  -80 

Remember to flip the inequality sign:

Solve Basic Inequality :

 6.3      Add  3  to both sides

             x > 3

Inequality Plot :

 6.4      Inequality plot for

         -8.000 X  + 24.000  >  0

  
 

One solution was found :