Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.8" was replaced by "(48/10)". 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 :

                (12/10)*(j+(35/10))-((48/10))≥0 

Step by step solution :

Step  1  :

            24
 Simplify   ——
            5 

Equation at the end of step  1  :

   12         35      24
  (—— • (j +  ——)) -  ——  ≥ 0 
   10         10      5 

Step  2  :

            7
 Simplify   —
            2

Equation at the end of step  2  :

   12         7      24
  (—— • (j +  —)) -  ——  ≥ 0 
   10         2      5 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  2  as the denominator :

          j     j • 2
     j =  —  =  —————
          1       2  

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:

 j • 2 + 7     2j + 7
 —————————  =  ——————
     2           2   

Equation at the end of step  3  :

   12   (2j + 7)     24
  (—— • ————————) -  ——  ≥ 0 
   10      2         5 

Step  4  :

            6
 Simplify   —
            5

Equation at the end of step  4  :

   6   (2j + 7)     24
  (— • ————————) -  ——  ≥ 0 
   5      2         5 

Step  5  :

Equation at the end of step  5  :

  3 • (2j + 7)    24
  ———————————— -  ——  ≥ 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:

 3 • (2j+7) - (24)     6j - 3
 —————————————————  =  ——————
         5               5   

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   6j - 3  =   3 • (2j - 1) 

Equation at the end of step  7  :

  3 • (2j - 1)
  ————————————  ≥ 0 
       5      

Step  8  :

 8.1    Multiply both sides by  5 

 8.2    Divide both sides by  3 

 8.3    Divide both sides by  2  

      j-(1/2)  ≥ 0

Solve Basic Inequality :

 8.4      Add  1/2  to both sides

             j ≥ 1/2

Inequality Plot :

 8.5      Inequality plot for

         1.200 X  - 0.600  ≥  0

  
 

One solution was found :