Solution - Adding, subtracting and finding the least common multiple

Rearrange:

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

                     x/4-(1-x/8)≥0 

Step by step solution :

Step  1  :

            x
 Simplify   —
            8

Equation at the end of step  1  :

  x          x
  — -  (1 -  —)  ≥ 0 
  4          8

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  8  as the denominator :

          1     1 • 8
     1 =  —  =  —————
          1       8  

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:

 8 - (x)     8 - x
 ———————  =  —————
    8          8  

Equation at the end of step  2  :

  x    (8 - x)
  — -  ———————  ≥ 0 
  4       8   

Step  3  :

            x
 Simplify   —
            4

Equation at the end of step  3  :

  x    (8 - x)
  — -  ———————  ≥ 0 
  4       8   

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       8 

      Least Common Multiple:
      8 

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 = 2

   Right_M = L.C.M / R_Deno = 1

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.      x • 2
   ——————————————————  =   —————
         L.C.M               8  

   R. Mult. • R. Num.      (8-x)
   ——————————————————  =   —————
         L.C.M               8  

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 x • 2 - ((8-x))     3x - 8
 ———————————————  =  ——————
        8              8   

Equation at the end of step  4  :

  3x - 8
  ——————  ≥ 0 
    8   

Step  5  :

 5.1    Multiply both sides by  8 

 5.2    Divide both sides by  3  

      x-(8/3)  ≥ 0

Solve Basic Inequality :

 5.3      Add  8/3  to both sides

             x ≥ 8/3

Inequality Plot :

 5.4      Inequality plot for

         0.375 x  - 1.000  ≥  0

  
 

One solution was found :