Solution - Adding, subtracting and finding the least common multiple

Rearrange:

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

                     7/2-(b+9/5)≥0 

Step by step solution :

Step  1  :

            9
 Simplify   —
            5

Equation at the end of step  1  :

  7          9
  — -  (b +  —)  ≥ 0 
  2          5

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  5  as the denominator :

          b     b • 5
     b =  —  =  —————
          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:

 b • 5 + 9     5b + 9
 —————————  =  ——————
     5           5   

Equation at the end of step  2  :

  7    (5b + 9)
  — -  ————————  ≥ 0 
  2       5    

Step  3  :

            7
 Simplify   —
            2

Equation at the end of step  3  :

  7    (5b + 9)
  — -  ————————  ≥ 0 
  2       5    

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       5 

      Least Common Multiple:
      10 

Calculating Multipliers :

 4.2    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 = 5

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 4.3      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.      7 • 5
   ——————————————————  =   —————
         L.C.M              10  

   R. Mult. • R. Num.      (5b+9) • 2
   ——————————————————  =   ——————————
         L.C.M                 10    

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 7 • 5 - ((5b+9) • 2)     17 - 10b
 ————————————————————  =  ————————
          10                 10   

Equation at the end of step  4  :

  17 - 10b
  ————————  ≥ 0 
     10   

Step  5  :

 5.1    Multiply both sides by  10 

 5.2    Multiply both sides by (-1)

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

      10b-17  ≤ 0

 5.3    Divide both sides by  10  

      b-(17/10)  ≤ 0

Solve Basic Inequality :

 5.4      Add  17/10  to both sides

             b ≤ 17/10

Inequality Plot :

 5.5      Inequality plot for

         -b  + 1.700  ≥  0

  
 

One solution was found :