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 :

                     1/4*a-1/2-(-1+1/2*a)<0 

Step by step solution :

Step  1  :

            1
 Simplify   —
            2

Equation at the end of step  1  :

    1    1       1
  ((—•a)-—)-(-1+(—•a))  < 0 
    4    2       2

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a fraction to a whole

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

           -1     -1 • 2
     -1 =  ——  =  ——————
           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 :

 2.2       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:

 -1 • 2 + a     a - 2
 ——————————  =  —————
     2            2  

Equation at the end of step  2  :

    1         1     (a - 2)
  ((— • a) -  —) -  ———————  < 0 
    4         2        2   

Step  3  :

            1
 Simplify   —
            2

Equation at the end of step  3  :

    1         1     (a - 2)
  ((— • a) -  —) -  ———————  < 0 
    4         2        2   

Step  4  :

            1
 Simplify   —
            4

Equation at the end of step  4  :

    1         1     (a - 2)
  ((— • a) -  —) -  ———————  < 0 
    4         2        2   

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       2 

      Least Common Multiple:
      4 

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 = 1

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 5.3      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.      a
   ——————————————————  =   —
         L.C.M             4

   R. Mult. • R. Num.      2
   ——————————————————  =   —
         L.C.M             4

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 a - (2)     a - 2
 ———————  =  —————
    4          4  

Equation at the end of step  5  :

  (a - 2)    (a - 2)
  ——————— -  ———————  < 0 
     4          2   

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       2 

      Least Common Multiple:
      4 

Calculating Multipliers :

 6.2    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 :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      (a-2)
   ——————————————————  =   —————
         L.C.M               4  

   R. Mult. • R. Num.      (a-2) • 2
   ——————————————————  =   —————————
         L.C.M                 4    

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 (a-2) - ((a-2) • 2)     2 - a
 ———————————————————  =  —————
          4                4  

Equation at the end of step  6  :

  2 - a
  —————  < 0 
    4  

Step  7  :

 7.1    Multiply both sides by  4 

 7.2    Multiply both sides by (-1)

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

      a-2  > 0

Solve Basic Inequality :

 7.3      Add  2  to both sides

             a > 2

Inequality Plot :

 7.4      Inequality plot for

         -0.250 a  + 0.500  <  0

  
 

One solution was found :