Solution - Adding, subtracting and finding the least common multiple

Rearrange:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

                     (2-5*x)/6-(3/5)>0 

Step by step solution :

Step  1  :

            3
 Simplify   —
            5

Equation at the end of step  1  :

  (2 - 5x)    3
  ———————— -  —  > 0 
     6        5

Step  2  :

            2 - 5x
 Simplify   ——————
              6   

Equation at the end of step  2  :

  (2 - 5x)    3
  ———————— -  —  > 0 
     6        5

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       6 

      The right denominator is :       5 

      Least Common Multiple:
      30 

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 = 5

   Right_M = L.C.M / R_Deno = 6

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.      (2-5x) • 5
   ——————————————————  =   ——————————
         L.C.M                 30    

   R. Mult. • R. Num.      3 • 6
   ——————————————————  =   —————
         L.C.M              30  

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:

 (2-5x) • 5 - (3 • 6)     -25x - 8
 ————————————————————  =  ————————
          30                 30   

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   -25x - 8  =   -1 • (25x + 8) 

Equation at the end of step  4  :

  -25x - 8
  ————————  > 0 
     30   

Step  5  :

 5.1    Multiply both sides by  30 

 5.2    Multiply both sides by (-1)

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

      25x+8  < 0

 5.3    Divide both sides by  25  

      x+(8/25)  < 0

Solve Basic Inequality :

 5.4      Subtract  8/25  from both sides

            x < -8/25

Inequality Plot :

 5.5      Inequality plot for

         -0.833 x  - 0.267  >  0

  
 

One solution was found :