Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.8" was replaced by "(18/10)". 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 :

                (24/10)*x-9-((18/10)*x+6)<0 

Step by step solution :

Step  1  :

            9
 Simplify   —
            5

Equation at the end of step  1  :

    24         9
  ((——•x)-9)-((—•x)+6)  < 0 
    10         5

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a whole to a fraction

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

         6     6 • 5
    6 =  —  =  —————
         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:

 9x + 6 • 5     9x + 30
 ——————————  =  ———————
     5             5   

Equation at the end of step  2  :

    24               (9x + 30)
  ((—— • x) -  9) -  —————————  < 0 
    10                   5    

Step  3  :

            12
 Simplify   ——
            5 

Equation at the end of step  3  :

    12               (9x + 30)
  ((—— • x) -  9) -  —————————  < 0 
    5                    5    

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

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

         9     9 • 5
    9 =  —  =  —————
         1       5  

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 12x - (9 • 5)     12x - 45
 —————————————  =  ————————
       5              5    

Equation at the end of step  4  :

  (12x - 45)    (9x + 30)
  —————————— -  —————————  < 0 
      5             5    

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   12x - 45  =   3 • (4x - 15) 

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   9x + 30  =   3 • (3x + 10) 

Adding fractions which have a common denominator :

 7.2       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:

 3 • (4x-15) - (3 • (3x+10))     3x - 75
 ———————————————————————————  =  ———————
              5                     5   

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   3x - 75  =   3 • (x - 25) 

Equation at the end of step  8  :

  3 • (x - 25)
  ————————————  < 0 
       5      

Step  9  :

 9.1    Multiply both sides by  5 

 9.2    Divide both sides by  3 

Solve Basic Inequality :

 9.3      Add  25  to both sides

             x < 25

Inequality Plot :

 9.4      Inequality plot for

         0.600 X  - 15.000  <  0

  
 

One solution was found :