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 :

                     -3/4-(y/8+11/4)<0 

Step by step solution :

Step  1  :

            11
 Simplify   ——
            4 

Equation at the end of step  1  :

        3      y    11
  (0 -  —) -  (— +  ——)  < 0 
        4      8    4 

Step  2  :

            y
 Simplify   —
            8

Equation at the end of step  2  :

        3      y    11
  (0 -  —) -  (— +  ——)  < 0 
        4      8    4 

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       8 

      The right denominator is :       4 

      Least Common Multiple:
      8 

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 = 1

   Right_M = L.C.M / R_Deno = 2

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.      y
   ——————————————————  =   —
         L.C.M             8

   R. Mult. • R. Num.      11 • 2
   ——————————————————  =   ——————
         L.C.M               8   

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:

 y + 11 • 2     y + 22
 ——————————  =  ——————
     8            8   

Equation at the end of step  3  :

        3     (y + 22)
  (0 -  —) -  ————————  < 0 
        4        8    

Step  4  :

            3
 Simplify   —
            4

Equation at the end of step  4  :

        3     (y + 22)
  (0 -  —) -  ————————  < 0 
        4        8    

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       8 

      Least Common Multiple:
      8 

Calculating Multipliers :

 5.2    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 = 1

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      -3 • 2
   ——————————————————  =   ——————
         L.C.M               8   

   R. Mult. • R. Num.      (y+22)
   ——————————————————  =   ——————
         L.C.M               8   

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 -3 • 2 - ((y+22))     -y - 28
 —————————————————  =  ———————
         8                8   

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -y - 28  =   -1 • (y + 28) 

Equation at the end of step  6  :

  -y - 28
  ———————  < 0 
     8   

Step  7  :

 7.1    Multiply both sides by  8 

 7.2    Multiply both sides by (-1)

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

      y+28  > 0

Solve Basic Inequality :

 7.3      Subtract  28  from both sides

            y > -28

Inequality Plot :

 7.4      Inequality plot for

         -0.125 y  - 3.500  <  0

  
 

One solution was found :