Solution - Adding, subtracting and finding the least common multiple

Rearrange:

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

                     2/5*x+2-(1/5-2*x)<0 

Step by step solution :

Step  1  :

            1
 Simplify   —
            5

Equation at the end of step  1  :

    2                1    
  ((— • x) +  2) -  (— -  2x)  < 0 
    5                5    

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a whole from a fraction

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

          2x     2x • 5
    2x =  ——  =  ——————
          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:

 1 - (2x • 5)     1 - 10x
 ————————————  =  ———————
      5              5   

Equation at the end of step  2  :

    2               (1 - 10x)
  ((— • x) +  2) -  —————————  < 0 
    5                   5    

Step  3  :

            2
 Simplify   —
            5

Equation at the end of step  3  :

    2               (1 - 10x)
  ((— • x) +  2) -  —————————  < 0 
    5                   5    

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

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

         2     2 • 5
    2 =  —  =  —————
         1       5  

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 2x + 2 • 5     2x + 10
 ——————————  =  ———————
     5             5   

Equation at the end of step  4  :

  (2x + 10)    (1 - 10x)
  ————————— -  —————————  < 0 
      5            5    

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   2x + 10  =   2 • (x + 5) 

Adding fractions which have a common denominator :

 6.2       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:

 2 • (x+5) - ((1-10x))     12x + 9
 —————————————————————  =  ———————
           5                  5   

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   12x + 9  =   3 • (4x + 3) 

Equation at the end of step  7  :

  3 • (4x + 3)
  ————————————  < 0 
       5      

Step  8  :

 8.1    Multiply both sides by  5 

 8.2    Divide both sides by  3 

 8.3    Divide both sides by  4  

      x+(3/4)  < 0

Solve Basic Inequality :

 8.4      Subtract  3/4  from both sides

            x < -3/4

Inequality Plot :

 8.5      Inequality plot for

         2.400 X  + 1.800  <  0

  
 

One solution was found :