Solution - Adding, subtracting and finding the least common multiple

Rearrange:

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

                     3/4-(1/2+n)≤0 

Step by step solution :

Step  1  :

            1
 Simplify   —
            2

Equation at the end of step  1  :

  3     1    
  — -  (— +  n)  ≤ 0 
  4     2    

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a whole to a fraction

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

         n     n • 2
    n =  —  =  —————
         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 + n • 2     2n + 1
 —————————  =  ——————
     2           2   

Equation at the end of step  2  :

  3    (2n + 1)
  — -  ————————  ≤ 0 
  4       2    

Step  3  :

            3
 Simplify   —
            4

Equation at the end of step  3  :

  3    (2n + 1)
  — -  ————————  ≤ 0 
  4       2    

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       2 

      Least Common Multiple:
      4 

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 = 1

   Right_M = L.C.M / R_Deno = 2

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.      3
   ——————————————————  =   —
         L.C.M             4

   R. Mult. • R. Num.      (2n+1) • 2
   ——————————————————  =   ——————————
         L.C.M                 4     

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 3 - ((2n+1) • 2)     1 - 4n
 ————————————————  =  ——————
        4               4   

Equation at the end of step  4  :

  1 - 4n
  ——————  ≤ 0 
    4   

Step  5  :

 5.1    Multiply both sides by  4 

 5.2    Multiply both sides by (-1)

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

      4n-1  ≥ 0

 5.3    Divide both sides by  4  

      n-(1/4)  ≥ 0

Solve Basic Inequality :

 5.4      Add  1/4  to both sides

             n ≥ 1/4

Inequality Plot :

 5.5      Inequality plot for

         -n  + 0.250  ≤  0

  
 

One solution was found :