Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "42.1" was replaced by "(421/10)". 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 :

                -(956/100)*x-((421/10))>0 

Step by step solution :

Step  1  :

            421
 Simplify   ———
            10 

Equation at the end of step  1  :

         956          421
  (0 -  (——— • x)) -  ———  > 0 
         100          10 

Step  2  :

            239
 Simplify   ———
            25 

Equation at the end of step  2  :

         239          421
  (0 -  (——— • x)) -  ———  > 0 
         25           10 

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       25 

      The right denominator is :       10 

      Least Common Multiple:
      50 

Calculating Multipliers :

 3.2    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 = 5

Making Equivalent Fractions :

 3.3      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.      -239x • 2
   ——————————————————  =   —————————
         L.C.M                50    

   R. Mult. • R. Num.      421 • 5
   ——————————————————  =   ———————
         L.C.M               50   

Adding fractions that have a common denominator :

 3.4       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:

 -239x • 2 - (421 • 5)     -478x - 2105
 —————————————————————  =  ————————————
          50                    50     

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   -478x - 2105  =   -1 • (478x + 2105) 

Equation at the end of step  4  :

  -478x - 2105
  ————————————  > 0 
       50     

Step  5  :

 5.1    Multiply both sides by  50 

 5.2    Multiply both sides by (-1)

Flip the inequality sign since you are multiplying by a negative number

      478x+2105  < 0

 5.3    Divide both sides by  478  

      x+(2105/478)  < 0

Solve Basic Inequality :

 5.4      Subtract  2105/478  from both sides

            x < -2105/478

Inequality Plot :

 5.5      Inequality plot for

         -9.560 x  - 42.100  >  0

  
 

One solution was found :