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)". 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 :

                -(8/10)*x-8-((2/10)*x)<0 

Step by step solution :

Step  1  :

            1
 Simplify   —
            5

Equation at the end of step  1  :

        8         1
  ((0-(——•x))-8)-(—•x)  < 0 
       10         5

Step  2  :

            4
 Simplify   —
            5

Equation at the end of step  2  :

          4                x
  ((0 -  (— • x)) -  8) -  —  < 0 
          5                5

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

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

         8     8 • 5
    8 =  —  =  —————
         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:

 -4x - (8 • 5)     -4x - 40
 —————————————  =  ————————
       5              5    

Equation at the end of step  3  :

  (-4x - 40)    x
  —————————— -  —  < 0 
      5         5

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   -4x - 40  =   -4 • (x + 10) 

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:

 -4 • (x+10) - (x)     -5x - 40
 —————————————————  =  ————————
         5                5    

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -5x - 40  =   -5 • (x + 8) 

Equation at the end of step  6  :

  -x - 8  < 0 

Step  7  :

 7.1    Multiply both sides by (-1)

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

      x+8  > 0

Solve Basic Inequality :

 7.2      Subtract  8  from both sides

            x > -8

Inequality Plot :

 7.3      Inequality plot for

         -x  - 8.000  <  0

  
 

One solution was found :