Solution - Adding, subtracting and finding the least common multiple

Rearrange:

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

                     2/7-(b+5/7)>0 

Step by step solution :

Step  1  :

            5
 Simplify   —
            7

Equation at the end of step  1  :

  2          5
  — -  (b +  —)  > 0 
  7          7

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  7  as the denominator :

          b     b • 7
     b =  —  =  —————
          1       7  

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:

 b • 7 + 5     7b + 5
 —————————  =  ——————
     7           7   

Equation at the end of step  2  :

  2    (7b + 5)
  — -  ————————  > 0 
  7       7    

Step  3  :

            2
 Simplify   —
            7

Equation at the end of step  3  :

  2    (7b + 5)
  — -  ————————  > 0 
  7       7    

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:

 2 - ((7b+5))     -7b - 3
 ————————————  =  ———————
      7              7   

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   -7b - 3  =   -1 • (7b + 3) 

Equation at the end of step  5  :

  -7b - 3
  ———————  > 0 
     7   

Step  6  :

 6.1    Multiply both sides by  7 

 6.2    Multiply both sides by (-1)

Flip the inequality sign since you are multiplying by a negative number

      7b+3  < 0

 6.3    Divide both sides by  7  

      b+(3/7)  < 0

Solve Basic Inequality :

 6.4      Subtract  3/7  from both sides

            b < -3/7

Inequality Plot :

 6.5      Inequality plot for

         -b  - 0.429  >  0

  
 

One solution was found :