Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.5" was replaced by "(15/10)". 2 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 :

                (125/100)*(c)+(15/10)-(89/12)>0 

Step by step solution :

Step  1  :

            89
 Simplify   ——
            12

Equation at the end of step  1  :

    125         15     89
  ((——— • c) +  ——) -  ——  > 0 
    100         10     12

Step  2  :

            3
 Simplify   —
            2

Equation at the end of step  2  :

    125         3     89
  ((——— • c) +  —) -  ——  > 0 
    100         2     12

Step  3  :

            5
 Simplify   —
            4

Equation at the end of step  3  :

    5         3     89
  ((— • c) +  —) -  ——  > 0 
    4         2     12

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       2 

      Least Common Multiple:
      4 

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 = 1

   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.      5c
   ——————————————————  =   ——
         L.C.M             4 

   R. Mult. • R. Num.      3 • 2
   ——————————————————  =   —————
         L.C.M               4  

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:

 5c + 3 • 2     5c + 6
 ——————————  =  ——————
     4            4   

Equation at the end of step  4  :

  (5c + 6)    89
  ———————— -  ——  > 0 
     4        12

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       12 

      Least Common Multiple:
      12 

Calculating Multipliers :

 5.2    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 = 3

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      (5c+6) • 3
   ——————————————————  =   ——————————
         L.C.M                 12    

   R. Mult. • R. Num.      89
   ——————————————————  =   ——
         L.C.M             12

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 (5c+6) • 3 - (89)     15c - 71
 —————————————————  =  ————————
        12                12   

Equation at the end of step  5  :

  15c - 71
  ————————  > 0 
     12   

Step  6  :

 6.1    Multiply both sides by  12 

 6.2    Divide both sides by  15  

      c-(71/15)  > 0

Solve Basic Inequality :

 6.3      Add  71/15  to both sides

             c > 71/15

Inequality Plot :

 6.4      Inequality plot for

         1.250 c  - 5.917  >  0

  
 

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