Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "21.3" was replaced by "(213/10)". 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 :

                     -r-(72/10)-((213/10))>0 

Step by step solution :

Step  1  :

            213
 Simplify   ———
            10 

Equation at the end of step  1  :

         72     213
  (-r -  ——) -  ———  > 0 
         10     10 

Step  2  :

            36
 Simplify   ——
            5 

Equation at the end of step  2  :

         36     213
  (-r -  ——) -  ———  > 0 
         5      10 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  5  as the denominator :

           -r     -r • 5
     -r =  ——  =  ——————
           1        5   

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 3.2       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:

 -r • 5 - (36)     -5r - 36
 —————————————  =  ————————
       5              5    

Equation at the end of step  3  :

  (-5r - 36)    213
  —————————— -  ———  > 0 
      5         10 

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   -5r - 36  =   -1 • (5r + 36) 

Calculating the Least Common Multiple :

 5.2    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       10 

      Least Common Multiple:
      10 

Calculating Multipliers :

 5.3    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 :

 5.4      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.      (-5r-36) • 2
   ——————————————————  =   ————————————
         L.C.M                  10     

   R. Mult. • R. Num.      213
   ——————————————————  =   ———
         L.C.M             10 

Adding fractions that have a common denominator :

 5.5       Adding up the two equivalent fractions

 (-5r-36) • 2 - (213)     -10r - 285
 ————————————————————  =  ——————————
          10                  10    

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -10r - 285  =   -5 • (2r + 57) 

Equation at the end of step  6  :

  -5 • (2r + 57)
  ——————————————  > 0 
        10      

Step  7  :

 7.1    Multiply both sides by  10 

 7.2    Divide both sides by  -5 

Remember to flip the inequality sign:

 7.3    Divide both sides by  2  

      r+(57/2)  < 0

Solve Basic Inequality :

 7.4      Subtract  57/2  from both sides

            r < -57/2

Inequality Plot :

 7.5      Inequality plot for

         -X  - 28.500  <  0

  
 

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