Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.8" was replaced by "(8/10)". 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 :

                     (16/10)-((8/10)*x+4)>0 

Step by step solution :

Step  1  :

            4
 Simplify   —
            5

Equation at the end of step  1  :

  16      4         
  —— -  ((— • x) +  4)  > 0 
  10      5         

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a whole to a fraction

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

         4     4 • 5
    4 =  —  =  —————
         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:

 4x + 4 • 5     4x + 20
 ——————————  =  ———————
     5             5   

Equation at the end of step  2  :

  16    (4x + 20)
  —— -  —————————  > 0 
  10        5    

Step  3  :

            8
 Simplify   —
            5

Equation at the end of step  3  :

  8    (4x + 20)
  — -  —————————  > 0 
  5        5    

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   4x + 20  =   4 • (x + 5) 

Adding fractions which have a common denominator :

 5.2       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:

 8 - (4 • (x+5))     -4x - 12
 ———————————————  =  ————————
        5               5    

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -4x - 12  =   -4 • (x + 3) 

Equation at the end of step  6  :

  -4 • (x + 3)
  ————————————  > 0 
       5      

Step  7  :

 7.1    Multiply both sides by  5 

 7.2    Divide both sides by  -4 

Remember to flip the inequality sign:

Solve Basic Inequality :

 7.3      Subtract  3  from both sides

            x < -3

Inequality Plot :

 7.4      Inequality plot for

         -0.800 X  - 2.400  <  0

  
 

One solution was found :