Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "9.2" was replaced by "(92/10)". 3 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 :

           4*v+6*v+(32/10)-((68/10)-(92/10))<0 

Step by step solution :

Step  1  :

            46
 Simplify   ——
            5 

Equation at the end of step  1  :

          32      68    46
  (10v +  ——) -  (—— -  ——)  < 0 
          10      10    5 

Step  2  :

            34
 Simplify   ——
            5 

Equation at the end of step  2  :

          32      34    46
  (10v +  ——) -  (—— -  ——)  < 0 
          10      5     5 

Step  3  :

Adding fractions which have a common denominator :

 3.1       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:

 34 - (46)     -12
 —————————  =  ———
     5          5 

Equation at the end of step  3  :

          32     -12
  (10v +  ——) -  ———  < 0 
          10      5 

Step  4  :

            16
 Simplify   ——
            5 

Equation at the end of step  4  :

          16     -12
  (10v +  ——) -  ———  < 0 
          5       5 

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Adding a fraction to a whole

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

            10v     10v • 5
     10v =  ———  =  ———————
             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 :

 5.2       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:

 10v • 5 + 16     50v + 16
 ————————————  =  ————————
      5              5    

Equation at the end of step  5  :

  (50v + 16)    -12
  —————————— -  ———  < 0 
      5          5 

Step  6  :

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   50v + 16  =   2 • (25v + 8) 

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:

 2 • (25v+8) - (-12)     50v + 28
 ———————————————————  =  ————————
          5                 5    

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   50v + 28  =   2 • (25v + 14) 

Equation at the end of step  8  :

  2 • (25v + 14)
  ——————————————  < 0 
        5       

Step  9  :

 9.1    Multiply both sides by  5 

 9.2    Divide both sides by  2 

 9.3    Divide both sides by  25  

      v+(14/25)  < 0

Solve Basic Inequality :

 9.4      Subtract  14/25  from both sides

            v < -14/25

Inequality Plot :

 9.5      Inequality plot for

         10.000 X  + 5.600  <  0

  
 

One solution was found :