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 :

                     15/16*x-((-5)/12)>0 

Step by step solution :

Step  1  :

            -5
 Simplify   ——
            12

Equation at the end of step  1  :

   15         -5
  (—— • x) -  ——  > 0 
   16         12

Step  2  :

            15
 Simplify   ——
            16

Equation at the end of step  2  :

   15         -5
  (—— • x) -  ——  > 0 
   16         12

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       16 

      The right denominator is :       12 

      Least Common Multiple:
      48 

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 = 3

   Right_M = L.C.M / R_Deno = 4

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.      15x • 3
   ——————————————————  =   ———————
         L.C.M               48   

   R. Mult. • R. Num.      -5 • 4
   ——————————————————  =   ——————
         L.C.M               48  

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:

 15x • 3 - (-5 • 4)     45x + 20
 ——————————————————  =  ————————
         48                48   

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   45x + 20  =   5 • (9x + 4) 

Equation at the end of step  4  :

  5 • (9x + 4)
  ————————————  > 0 
       48     

Step  5  :

 5.1    Multiply both sides by  48 

 5.2    Divide both sides by  5 

 5.3    Divide both sides by  9  

      x+(4/9)  > 0

Solve Basic Inequality :

 5.4      Subtract  4/9  from both sides

            x > -4/9

Inequality Plot :

 5.5      Inequality plot for

         0.938 X  + 0.417  >  0

  
 

One solution was found :