Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.2" was replaced by "(2/10)". 3 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 :

           -(51/10)-(87/10)*t-(-5*((2/10)*t-19))<0 

Step by step solution :

Step  1  :

            1
 Simplify   —
            5

Equation at the end of step  1  :

      51   87             1
  ((0-——)-(——•t))-(0-(5•((—•t)-19)))  < 0 
      10   10             5

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a whole from a fraction

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

          19     19 • 5
    19 =  ——  =  ——————
          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 :

 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:

 t - (19 • 5)     t - 95
 ————————————  =  ——————
      5             5   

Equation at the end of step  2  :

      51   87           (t-95)
  ((0-——)-(——•t))-(0-(5•——————))  < 0 
      10   10             5   

Step  3  :

Equation at the end of step  3  :

      51   87
  ((0-——)-(——•t))-(0-(t-95))  < 0 
      10   10

Step  4  :

            87
 Simplify   ——
            10

Equation at the end of step  4  :

         51      87          
  ((0 -  ——) -  (—— • t)) -  (95 - t)  < 0 
         10      10          

Step  5  :

            51
 Simplify   ——
            10

Equation at the end of step  5  :

         51     87t     
  ((0 -  ——) -  ———) -  (95 - t)  < 0 
         10     10      

Step  6  :

Adding fractions which have a common denominator :

 6.1       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:

 -51 - (87t)     -87t - 51
 ———————————  =  —————————
     10             10    

Equation at the end of step  6  :

  (-87t - 51)    
  ——————————— -  (95 - t)  < 0 
      10         

Step  7  :

Rewriting the whole as an Equivalent Fraction :

 7.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  10  as the denominator :

              95 - t     (95 - t) • 10
    95 - t =  ——————  =  —————————————
                1             10      

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   -87t - 51  =   -3 • (29t + 17) 

Adding fractions that have a common denominator :

 8.2       Adding up the two equivalent fractions

 -3 • (29t+17) - ((95-t) • 10)     -77t - 1001
 —————————————————————————————  =  ———————————
              10                       10     

Step  9  :

Pulling out like terms :

 9.1     Pull out like factors :

   -77t - 1001  =   -77 • (t + 13) 

Equation at the end of step  9  :

  -77 • (t + 13)
  ——————————————  < 0 
        10      

Step  10  :

 10.1    Multiply both sides by  10 

 10.2    Divide both sides by  -77 

Remember to flip the inequality sign:

Solve Basic Inequality :

 10.3      Subtract  13  from both sides

            t > -13

Inequality Plot :

 10.4      Inequality plot for

         -7.700 X  - 100.100  >  0

  
 

One solution was found :