Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.7" was replaced by "(27/10)". 2 more similar replacement(s)

Rearrange:

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

                -1*t-(669/100)-(-(27/10))>0 

Step by step solution :

Step  1  :

            27
 Simplify   ——
            10

Equation at the end of step  1  :

         669           27
  (-t -  ———) -  (0 -  ——)  > 0 
         100           10

Step  2  :

            669
 Simplify   ———
            100

Equation at the end of step  2  :

         669     -27
  (-t -  ———) -  ———  > 0 
         100     10 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  100  as the denominator :

           -t     -t • 100
     -t =  ——  =  ————————
           1        100   

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:

 -t • 100 - (669)     -100t - 669
 ————————————————  =  ———————————
       100                100    

Equation at the end of step  3  :

  (-100t - 669)    -27
  ————————————— -  ———  > 0 
       100         10 

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   -100t - 669  =   -1 • (100t + 669) 

Calculating the Least Common Multiple :

 5.2    Find the Least Common Multiple

      The left denominator is :       100 

      The right denominator is :       10 

      Least Common Multiple:
      100 

Calculating Multipliers :

 5.3    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 = 10

Making Equivalent Fractions :

 5.4      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.      (-100t-669)
   ——————————————————  =   ———————————
         L.C.M                 100    

   R. Mult. • R. Num.      -27 • 10
   ——————————————————  =   ————————
         L.C.M               100   

Adding fractions that have a common denominator :

 5.5       Adding up the two equivalent fractions

 (-100t-669) - (-27 • 10)     -100t - 399
 ————————————————————————  =  ———————————
           100                    100    

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -100t - 399  =   -1 • (100t + 399) 

Equation at the end of step  6  :

  -100t - 399
  ———————————  > 0 
      100    

Step  7  :

 7.1    Multiply both sides by  100 

 7.2    Multiply both sides by (-1)

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

      100t+399  < 0

 7.3    Divide both sides by  100  

      t+(399/100)  < 0

Solve Basic Inequality :

 7.4      Subtract  399/100  from both sides

            t < -399/100

Inequality Plot :

 7.5      Inequality plot for

         -t  - 3.990  >  0

  
 

One solution was found :