Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.3" was replaced by "(23/10)". 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 :

                     (69/10)-(w-(23/10))<0 

Step by step solution :

Step  1  :

            23
 Simplify   ——
            10

Equation at the end of step  1  :

  69          23
  —— -  (w -  ——)  < 0 
  10          10

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

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

          w     w • 10
     w =  —  =  ——————
          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 :

 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:

 w • 10 - (23)     10w - 23
 —————————————  =  ————————
      10              10   

Equation at the end of step  2  :

  69    (10w - 23)
  —— -  ——————————  < 0 
  10        10    

Step  3  :

            69
 Simplify   ——
            10

Equation at the end of step  3  :

  69    (10w - 23)
  —— -  ——————————  < 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:

 69 - ((10w-23))     92 - 10w
 ———————————————  =  ————————
       10               10   

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   92 - 10w  =   -2 • (5w - 46) 

Equation at the end of step  5  :

  -2 • (5w - 46)
  ——————————————  < 0 
        10      

Step  6  :

 6.1    Multiply both sides by  10 

 6.2    Divide both sides by  -2 

Remember to flip the inequality sign:

 6.3    Divide both sides by  5  

      w-(46/5)  > 0

Solve Basic Inequality :

 6.4      Add  46/5  to both sides

             w > 46/5

Inequality Plot :

 6.5      Inequality plot for

         -X  + 9.200  >  0

  
 

One solution was found :