Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "22.2" was replaced by "(222/10)". 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 :

                (33/10)*w-9-(-(222/10))>0 

Step by step solution :

Step  1  :

            111
 Simplify   ———
             5 

Equation at the end of step  1  :

    33                     111
  ((—— • w) -  9) -  (0 -  ———)  > 0 
    10                      5 

Step  2  :

            33
 Simplify   ——
            10

Equation at the end of step  2  :

    33               -111
  ((—— • w) -  9) -  ————  > 0 
    10                5  

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

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

         9     9 • 10
    9 =  —  =  ——————
         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:

 33w - (9 • 10)     33w - 90
 ——————————————  =  ————————
       10              10   

Equation at the end of step  3  :

  (33w - 90)    -111
  —————————— -  ————  > 0 
      10         5  

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   33w - 90  =   3 • (11w - 30) 

Calculating the Least Common Multiple :

 5.2    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       5 

      Least Common Multiple:
      10 

Calculating Multipliers :

 5.3    Calculate multipliers for the two fractions


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = 1

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 5.4      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)²   and  (y²+y)/(y+1)³  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

   L. Mult. • L. Num.      3 • (11w-30)
   ——————————————————  =   ————————————
         L.C.M                  10     

   R. Mult. • R. Num.      -111 • 2
   ——————————————————  =   ————————
         L.C.M                10   

Adding fractions that have a common denominator :

 5.5       Adding up the two equivalent fractions

 3 • (11w-30) - (-111 • 2)     33w + 132
 —————————————————————————  =  —————————
            10                    10    

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   33w + 132  =   33 • (w + 4) 

Equation at the end of step  6  :

  33 • (w + 4)
  ————————————  > 0 
       10     

Step  7  :

 7.1    Multiply both sides by  10 

 7.2    Divide both sides by  33 

Solve Basic Inequality :

 7.3      Subtract  4  from both sides

            w > -4

Inequality Plot :

 7.4      Inequality plot for

         3.300 X  + 13.200  >  0

  
 

One solution was found :