Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "15.2" was replaced by "(152/10)". 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 :

                     x+(113/10)-((152/10))>0 

Step by step solution :

Step  1  :

            76
 Simplify   ——
            5 

Equation at the end of step  1  :

        113     76
  (x +  ———) -  ——  > 0 
        10      5 

Step  2  :

            113
 Simplify   ———
            10 

Equation at the end of step  2  :

        113     76
  (x +  ———) -  ——  > 0 
        10      5 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  10  as the denominator :

          x     x • 10
     x =  —  =  ——————
          1       10  

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:

 x • 10 + 113     10x + 113
 ————————————  =  —————————
      10             10    

Equation at the end of step  3  :

  (10x + 113)    76
  ——————————— -  ——  > 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.      (10x+113)
   ——————————————————  =   —————————
         L.C.M                10    

   R. Mult. • R. Num.      76 • 2
   ——————————————————  =   ——————
         L.C.M               10  

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (10x+113) - (76 • 2)     10x - 39
 ————————————————————  =  ————————
          10                 10   

Equation at the end of step  4  :

  10x - 39
  ————————  > 0 
     10   

Step  5  :

 5.1    Multiply both sides by  10 

 5.2    Divide both sides by  10  

      x-(39/10)  > 0

Solve Basic Inequality :

 5.3      Add  39/10  to both sides

             x > 39/10

Inequality Plot :

 5.4      Inequality plot for

         x  - 3.900  >  0

  
 

One solution was found :