Solution - Adding, subtracting and finding the least common multiple

Rearrange:

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

                     3/7*a-(76/5)≤0 

Step by step solution :

Step  1  :

            76
 Simplify   ——
            5 

Equation at the end of step  1  :

   3         76
  (— • a) -  ——  ≤ 0 
   7         5 

Step  2  :

            3
 Simplify   —
            7

Equation at the end of step  2  :

   3         76
  (— • a) -  ——  ≤ 0 
   7         5 

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       7 

      The right denominator is :       5 

      Least Common Multiple:
      35 

Calculating Multipliers :

 3.2    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 = 7

Making Equivalent Fractions :

 3.3      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.      3a • 5
   ——————————————————  =   ——————
         L.C.M               35  

   R. Mult. • R. Num.      76 • 7
   ——————————————————  =   ——————
         L.C.M               35  

Adding fractions that have a common denominator :

 3.4       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:

 3a • 5 - (76 • 7)     15a - 532
 —————————————————  =  —————————
        35                35    

Equation at the end of step  3  :

  15a - 532
  —————————  ≤ 0 
     35    

Step  4  :

 4.1    Multiply both sides by  35 

 4.2    Divide both sides by  15  

      a-(532/15)  ≤ 0

Solve Basic Inequality :

 4.3      Add  532/15  to both sides

             a ≤ 532/15

Inequality Plot :

 4.4      Inequality plot for

         0.429 a  - 15.200  ≤  0

  
 

One solution was found :