Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.2" was replaced by "(22/10)". 3 more similar replacement(s)

Rearrange:

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

                (18/10)-(4/10)*y-((22/10)-2*y)≥0 

Step by step solution :

Step  1  :

            11
 Simplify   ——
            5 

Equation at the end of step  1  :

   18   4      11
  (——-(——•y))-(——-2y)  ≥ 0 
   10  10      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 :

          2y     2y • 5
    2y =  ——  =  ——————
          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:

 11 - (2y • 5)     11 - 10y
 —————————————  =  ————————
       5              5    

Equation at the end of step  2  :

   18      4          (11 - 10y)
  (—— -  (—— • y)) -  ——————————  ≥ 0 
   10     10              5     

Step  3  :

            2
 Simplify   —
            5

Equation at the end of step  3  :

   18     2          (11 - 10y)
  (—— -  (— • y)) -  ——————————  ≥ 0 
   10     5              5     

Step  4  :

            9
 Simplify   —
            5

Equation at the end of step  4  :

   9    2y     (11 - 10y)
  (— -  ——) -  ——————————  ≥ 0 
   5    5          5     

Step  5  :

Adding fractions which have a common denominator :

 5.1       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:

 9 - (2y)     9 - 2y
 ————————  =  ——————
    5           5   

Equation at the end of step  5  :

  (9 - 2y)    (11 - 10y)
  ———————— -  ——————————  ≥ 0 
     5            5     

Step  6  :

Adding fractions which have a common denominator :

 6.1       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:

 (9-2y) - ((11-10y))     8y - 2
 ———————————————————  =  ——————
          5                5   

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   8y - 2  =   2 • (4y - 1) 

Equation at the end of step  7  :

  2 • (4y - 1)
  ————————————  ≥ 0 
       5      

Step  8  :

 8.1    Multiply both sides by  5 

 8.2    Divide both sides by  2 

 8.3    Divide both sides by  4  

      y-(1/4)  ≥ 0

Solve Basic Inequality :

 8.4      Add  1/4  to both sides

             y ≥ 1/4

Inequality Plot :

 8.5      Inequality plot for

         1.600 X  - 0.400  ≥  0

  
 

One solution was found :