Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "6.9" was replaced by "(69/10)". 3 more similar replacement(s)

Rearrange:

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

                (65/10)*x-(11/10)-((69/10))>0 

Step by step solution :

Step  1  :

            69
 Simplify   ——
            10

Equation at the end of step  1  :

    65         11     69
  ((—— • x) -  ——) -  ——  > 0 
    10         10     10

Step  2  :

            11
 Simplify   ——
            10

Equation at the end of step  2  :

    65         11     69
  ((—— • x) -  ——) -  ——  > 0 
    10         10     10

Step  3  :

            13
 Simplify   ——
            2 

Equation at the end of step  3  :

    13         11     69
  ((—— • x) -  ——) -  ——  > 0 
    2          10     10

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       10 

      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 = 1

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.      13x • 5
   ——————————————————  =   ———————
         L.C.M               10   

   R. Mult. • R. Num.      11
   ——————————————————  =   ——
         L.C.M             10

Adding fractions that have a common denominator :

 4.4       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:

 13x • 5 - (11)     65x - 11
 ——————————————  =  ————————
       10              10   

Equation at the end of step  4  :

  (65x - 11)    69
  —————————— -  ——  > 0 
      10        10

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:

 (65x-11) - (69)     65x - 80
 ———————————————  =  ————————
       10               10   

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   65x - 80  =   5 • (13x - 16) 

Equation at the end of step  6  :

  5 • (13x - 16)
  ——————————————  > 0 
        10      

Step  7  :

 7.1    Multiply both sides by  10 

 7.2    Divide both sides by  5 

 7.3    Divide both sides by  13  

      x-(16/13)  > 0

Solve Basic Inequality :

 7.4      Add  16/13  to both sides

             x > 16/13

Inequality Plot :

 7.5      Inequality plot for

         6.500 X  - 8.000  >  0

  
 

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