Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "8.5" was replaced by "(85/10)". 4 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 :

           (175/100)*x+(35/10)-((325/100)*x-(85/10))>0 

Step by step solution :

Step  1  :

            17
 Simplify   ——
            2 

Equation at the end of step  1  :

    175    35    325    17
  ((———•x)+——)-((———•x)-——)  > 0 
    100    10    100    2 

Step  2  :

            13
 Simplify   ——
            4 

Equation at the end of step  2  :

    175    35    13    17
  ((———•x)+——)-((——•x)-——)  > 0 
    100    10    4     2 

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       2 

      Least Common Multiple:
      4 

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 = 1

   Right_M = L.C.M / R_Deno = 2

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.      13x
   ——————————————————  =   ———
         L.C.M              4 

   R. Mult. • R. Num.      17 • 2
   ——————————————————  =   ——————
         L.C.M               4   

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:

 13x - (17 • 2)     13x - 34
 ——————————————  =  ————————
       4               4    

Equation at the end of step  3  :

    175         35     (13x - 34)
  ((——— • x) +  ——) -  ——————————  > 0 
    100         10         4     

Step  4  :

            7
 Simplify   —
            2

Equation at the end of step  4  :

    175         7     (13x - 34)
  ((——— • x) +  —) -  ——————————  > 0 
    100         2         4     

Step  5  :

            7
 Simplify   —
            4

Equation at the end of step  5  :

    7         7     (13x - 34)
  ((— • x) +  —) -  ——————————  > 0 
    4         2         4     

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       2 

      Least Common Multiple:
      4 

Calculating Multipliers :

 6.2    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 = 1

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      7x
   ——————————————————  =   ——
         L.C.M             4 

   R. Mult. • R. Num.      7 • 2
   ——————————————————  =   —————
         L.C.M               4  

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 7x + 7 • 2     7x + 14
 ——————————  =  ———————
     4             4   

Equation at the end of step  6  :

  (7x + 14)    (13x - 34)
  ————————— -  ——————————  > 0 
      4            4     

Step  7  :

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   7x + 14  =   7 • (x + 2) 

Adding fractions which have a common denominator :

 8.2       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:

 7 • (x+2) - ((13x-34))     48 - 6x
 ——————————————————————  =  ———————
           4                   4   

Step  9  :

Pulling out like terms :

 9.1     Pull out like factors :

   48 - 6x  =   -6 • (x - 8) 

Equation at the end of step  9  :

  -6 • (x - 8)
  ————————————  > 0 
       4      

Step  10  :

 10.1    Multiply both sides by  4 

 10.2    Divide both sides by  -6 

Remember to flip the inequality sign:

Solve Basic Inequality :

 10.3      Add  8  to both sides

             x < 8

Inequality Plot :

 10.4      Inequality plot for

         -1.500 X  + 12.000  <  0

  
 

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