Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "5.8" was replaced by "(58/10)". 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 :

                3*d-7*d+(28/10)-((58/10)-27)<0 

Step by step solution :

Step  1  :

            29
 Simplify   ——
            5 

Equation at the end of step  1  :

          28      29    
  (-4d +  ——) -  (—— -  27)  < 0 
          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 :

          27     27 • 5
    27 =  ——  =  ——————
          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:

 29 - (27 • 5)     -106
 —————————————  =  ————
       5            5  

Equation at the end of step  2  :

          28     -106
  (-4d +  ——) -  ————  < 0 
          10      5  

Step  3  :

            14
 Simplify   ——
            5 

Equation at the end of step  3  :

          14     -106
  (-4d +  ——) -  ————  < 0 
          5       5  

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a fraction to a whole

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

            -4d     -4d • 5
     -4d =  ———  =  ———————
             1         5   

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 -4d • 5 + 14     14 - 20d
 ————————————  =  ————————
      5              5    

Equation at the end of step  4  :

  (14 - 20d)    -106
  —————————— -  ————  < 0 
      5          5  

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   14 - 20d  =   -2 • (10d - 7) 

Adding fractions which have a common denominator :

 6.2       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:

 -2 • (10d-7) - (-106)     120 - 20d
 —————————————————————  =  —————————
           5                   5    

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   120 - 20d  =   -20 • (d - 6) 

Equation at the end of step  7  :

  -20 • (d - 6)
  —————————————  < 0 
        5      

Step  8  :

 8.1    Multiply both sides by  5 

 8.2    Divide both sides by  -20 

Remember to flip the inequality sign:

Solve Basic Inequality :

 8.3      Add  6  to both sides

             d > 6

Inequality Plot :

 8.4      Inequality plot for

         -4.000 X  + 24.000  >  0

  
 

One solution was found :