Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "11.3" was replaced by "(113/10)". 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 :

                (65/10)+2*x-(-(113/10))<0 

Step by step solution :

Step  1  :

            113
 Simplify   ———
            10 

Equation at the end of step  1  :

   65                 113
  (—— +  2x) -  (0 -  ———)  < 0 
   10                 10 

Step  2  :

            13
 Simplify   ——
            2 

Equation at the end of step  2  :

   13           -113
  (—— +  2x) -  ————  < 0 
   2             10 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  2  as the denominator :

          2x     2x • 2
    2x =  ——  =  ——————
          1        2   

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:

 13 + 2x • 2     4x + 13
 ———————————  =  ———————
      2             2   

Equation at the end of step  3  :

  (4x + 13)    -113
  ————————— -  ————  < 0 
      2         10 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       10 

      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 = 5

   Right_M = L.C.M / R_Deno = 1

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.      (4x+13) • 5
   ——————————————————  =   ———————————
         L.C.M                 10     

   R. Mult. • R. Num.      -113
   ——————————————————  =   ————
         L.C.M              10 

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (4x+13) • 5 - (-113)     20x + 178
 ————————————————————  =  —————————
          10                 10    

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   20x + 178  =   2 • (10x + 89) 

Equation at the end of step  5  :

  2 • (10x + 89)
  ——————————————  < 0 
        10      

Step  6  :

 6.1    Multiply both sides by  10 

 6.2    Divide both sides by  2 

 6.3    Divide both sides by  10  

      x+(89/10)  < 0

Solve Basic Inequality :

 6.4      Subtract  89/10  from both sides

            x < -89/10

Inequality Plot :

 6.5      Inequality plot for

         2.000 X  + 17.800  <  0

  
 

One solution was found :