Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.9" was replaced by "(19/10)". 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 :

                -(12/10)*r-(53/10)-((19/10))>0 

Step by step solution :

Step  1  :

            19
 Simplify   ——
            10

Equation at the end of step  1  :

       12     53  19
  ((0-(——•r))-——)-——  > 0 
       10     10  10

Step  2  :

            53
 Simplify   ——
            10

Equation at the end of step  2  :

          12          53     19
  ((0 -  (—— • r)) -  ——) -  ——  > 0 
          10          10     10

Step  3  :

            6
 Simplify   —
            5

Equation at the end of step  3  :

          6          53     19
  ((0 -  (— • r)) -  ——) -  ——  > 0 
          5          10     10

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       5 

      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 = 2

   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.      -6r • 2
   ——————————————————  =   ———————
         L.C.M               10   

   R. Mult. • R. Num.      53
   ——————————————————  =   ——
         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:

 -6r • 2 - (53)     -12r - 53
 ——————————————  =  —————————
       10              10    

Equation at the end of step  4  :

  (-12r - 53)    19
  ——————————— -  ——  > 0 
      10         10

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -12r - 53  =   -1 • (12r + 53) 

Adding fractions which have a common denominator :

 6.2       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:

 (-12r-53) - (19)     -12r - 72
 ————————————————  =  —————————
        10               10    

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   -12r - 72  =   -12 • (r + 6) 

Equation at the end of step  7  :

  -12 • (r + 6)
  —————————————  > 0 
       10      

Step  8  :

 8.1    Multiply both sides by  10 

 8.2    Divide both sides by  -12 

Remember to flip the inequality sign:

Solve Basic Inequality :

 8.3      Subtract  6  from both sides

            r < -6

Inequality Plot :

 8.4      Inequality plot for

         -1.200 X  - 7.200  <  0

  
 

One solution was found :