Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.5" was replaced by "(15/10)". 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 :

                     14-(6/10)*t-((15/10))<0 

Step by step solution :

Step  1  :

            3
 Simplify   —
            2

Equation at the end of step  1  :

           6          3
  (14 -  (—— • t)) -  —  < 0 
          10          2

Step  2  :

            3
 Simplify   —
            5

Equation at the end of step  2  :

          3          3
  (14 -  (— • t)) -  —  < 0 
          5          2

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  5  as the denominator :

           14     14 • 5
     14 =  ——  =  ——————
           1        5   

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:

 14 • 5 - (3t)     70 - 3t
 —————————————  =  ———————
       5              5   

Equation at the end of step  3  :

  (70 - 3t)    3
  ————————— -  —  < 0 
      5        2

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       2 

      Least Common Multiple:
      10 

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 = 5

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.      (70-3t) • 2
   ——————————————————  =   ———————————
         L.C.M                 10     

   R. Mult. • R. Num.      3 • 5
   ——————————————————  =   —————
         L.C.M              10  

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (70-3t) • 2 - (3 • 5)     125 - 6t
 —————————————————————  =  ————————
          10                  10   

Equation at the end of step  4  :

  125 - 6t
  ————————  < 0 
     10   

Step  5  :

 5.1    Multiply both sides by  10 

 5.2    Multiply both sides by (-1)

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

      6t-125  > 0

 5.3    Divide both sides by  6  

      t-(125/6)  > 0

Solve Basic Inequality :

 5.4      Add  125/6  to both sides

             t > 125/6

Inequality Plot :

 5.5      Inequality plot for

         -0.600 t  + 12.500  <  0

  
 

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