Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.6" was replaced by "(16/10)". 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 :

                     x+(54/10)-(-(16/10))<0 

Step by step solution :

Step  1  :

            8
 Simplify   —
            5

Equation at the end of step  1  :

        54           8
  (x +  ——) -  (0 -  —)  < 0 
        10           5

Step  2  :

            27
 Simplify   ——
            5 

Equation at the end of step  2  :

        27     -8
  (x +  ——) -  ——  < 0 
        5      5 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole

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

          x     x • 5
     x =  —  =  —————
          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:

 x • 5 + 27     5x + 27
 ——————————  =  ———————
     5             5   

Equation at the end of step  3  :

  (5x + 27)    -8
  ————————— -  ——  < 0 
      5        5 

Step  4  :

Adding fractions which have a common denominator :

 4.1       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:

 (5x+27) - (-8)     5x + 35
 ——————————————  =  ———————
       5               5   

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   5x + 35  =   5 • (x + 7) 

Equation at the end of step  5  :

  x + 7  < 0 

Step  6  :

Solve Basic Inequality :

 6.1      Subtract  7  from both sides

            x < -7

Inequality Plot :

 6.2      Inequality plot for

         x  + 7.000  <  0

  
 

One solution was found :