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 :

                     2/3*t-1/6-(5/6)≤0 

Step by step solution :

Step  1  :

            5
 Simplify   —
            6

Equation at the end of step  1  :

    2         1     5
  ((— • t) -  —) -  —  ≤ 0 
    3         6     6

Step  2  :

            1
 Simplify   —
            6

Equation at the end of step  2  :

    2         1     5
  ((— • t) -  —) -  —  ≤ 0 
    3         6     6

Step  3  :

            2
 Simplify   —
            3

Equation at the end of step  3  :

    2         1     5
  ((— • t) -  —) -  —  ≤ 0 
    3         6     6

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       3 

      The right denominator is :       6 

      Least Common Multiple:
      6 

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.      2t • 2
   ——————————————————  =   ——————
         L.C.M               6   

   R. Mult. • R. Num.      1
   ——————————————————  =   —
         L.C.M             6

Adding fractions that have a common denominator :

 4.4       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:

 2t • 2 - (1)     4t - 1
 ————————————  =  ——————
      6             6   

Equation at the end of step  4  :

  (4t - 1)    5
  ———————— -  —  ≤ 0 
     6        6

Step  5  :

Adding fractions which have a common denominator :

 5.1       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 (4t-1) - (5)     4t - 6
 ————————————  =  ——————
      6             6   

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   4t - 6  =   2 • (2t - 3) 

Equation at the end of step  6  :

  2 • (2t - 3)
  ————————————  ≤ 0 
       6      

Step  7  :

 7.1    Multiply both sides by  6 

 7.2    Divide both sides by  2 

 7.3    Divide both sides by  2  

      t-(3/2)  ≤ 0

Solve Basic Inequality :

 7.4      Add  3/2  to both sides

             t ≤ 3/2

Inequality Plot :

 7.5      Inequality plot for

         0.667 X  - 1.000  ≤  0

  
 

One solution was found :