Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "23.4" was replaced by "(234/10)". 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 :

           4*((18/10)*z+(225/100))-((234/10))<0 

Step by step solution :

Step  1  :

            117
 Simplify   ———
             5 

Equation at the end of step  1  :

       18    225   117
  (4•((——•z)+———))-———  < 0 
       10    100    5 

Step  2  :

            9
 Simplify   —
            4

Equation at the end of step  2  :

         18         9      117
  (4 • ((—— • z) +  —)) -  ———  < 0 
         10         4       5 

Step  3  :

            9
 Simplify   —
            5

Equation at the end of step  3  :

         9         9      117
  (4 • ((— • z) +  —)) -  ———  < 0 
         5         4       5 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       4 

      Least Common Multiple:
      20 

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 = 4

   Right_M = L.C.M / R_Deno = 5

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.      9z • 4
   ——————————————————  =   ——————
         L.C.M               20  

   R. Mult. • R. Num.      9 • 5
   ——————————————————  =   —————
         L.C.M              20  

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:

 9z • 4 + 9 • 5     36z + 45
 ——————————————  =  ————————
       20              20   

Equation at the end of step  4  :

       (36z + 45)     117
  (4 • ——————————) -  ———  < 0 
           20          5 

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   36z + 45  =   9 • (4z + 5) 

Equation at the end of step  6  :

  9 • (4z + 5)    117
  ———————————— -  ———  < 0 
       5           5 

Step  7  :

Adding fractions which have a common denominator :

 7.1       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:

 9 • (4z+5) - (117)     36z - 72
 ——————————————————  =  ————————
         5                 5    

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   36z - 72  =   36 • (z - 2) 

Equation at the end of step  8  :

  36 • (z - 2)
  ————————————  < 0 
       5      

Step  9  :

 9.1    Multiply both sides by  5 

 9.2    Divide both sides by  36 

Solve Basic Inequality :

 9.3      Add  2  to both sides

             z < 2

Inequality Plot :

 9.4      Inequality plot for

         7.200 X  - 14.400  <  0

  
 

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