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 :

                     1/4+m-(1/2)≤0 

Step by step solution :

Step  1  :

            1
 Simplify   —
            2

Equation at the end of step  1  :

   1          1
  (— +  m) -  —  ≤ 0 
   4          2

Step  2  :

            1
 Simplify   —
            4

Equation at the end of step  2  :

   1          1
  (— +  m) -  —  ≤ 0 
   4          2

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  4  as the denominator :

         m     m • 4
    m =  —  =  —————
         1       4  

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 :

 3.2       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 + m • 4     4m + 1
 —————————  =  ——————
     4           4   

Equation at the end of step  3  :

  (4m + 1)    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.      (4m+1)
   ——————————————————  =   ——————
         L.C.M               4   

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

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (4m+1) - (2)     4m - 1
 ————————————  =  ——————
      4             4   

Equation at the end of step  4  :

  4m - 1
  ——————  ≤ 0 
    4   

Step  5  :

 5.1    Multiply both sides by  4 

 5.2    Divide both sides by  4  

      m-(1/4)  ≤ 0

Solve Basic Inequality :

 5.3      Add  1/4  to both sides

             m ≤ 1/4

Inequality Plot :

 5.4      Inequality plot for

         m  - 0.250  ≤  0

  
 

One solution was found :