Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.8" was replaced by "(18/10)". 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 :

                     (143/10)-(k+(18/10))<0 

Step by step solution :

Step  1  :

            9
 Simplify   —
            5

Equation at the end of step  1  :

  143          9
  ——— -  (k +  —)  < 0 
  10           5

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a fraction to a whole

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

          k     k • 5
     k =  —  =  —————
          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 :

 2.2       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:

 k • 5 + 9     5k + 9
 —————————  =  ——————
     5           5   

Equation at the end of step  2  :

  143    (5k + 9)
  ——— -  ————————  < 0 
  10        5    

Step  3  :

            143
 Simplify   ———
            10 

Equation at the end of step  3  :

  143    (5k + 9)
  ——— -  ————————  < 0 
  10        5    

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       5 

      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 = 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.      143
   ——————————————————  =   ———
         L.C.M             10 

   R. Mult. • R. Num.      (5k+9) • 2
   ——————————————————  =   ——————————
         L.C.M                 10    

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 143 - ((5k+9) • 2)     125 - 10k
 ——————————————————  =  —————————
         10                10    

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   125 - 10k  =   -5 • (2k - 25) 

Equation at the end of step  5  :

  -5 • (2k - 25)
  ——————————————  < 0 
        10      

Step  6  :

 6.1    Multiply both sides by  10 

 6.2    Divide both sides by  -5 

Remember to flip the inequality sign:

 6.3    Divide both sides by  2  

      k-(25/2)  > 0

Solve Basic Inequality :

 6.4      Add  25/2  to both sides

             k > 25/2

Inequality Plot :

 6.5      Inequality plot for

         -X  + 12.500  >  0

  
 

One solution was found :