Solution - Adding, subtracting and finding the least common multiple

Rearrange:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

                     -1/4*x-8-(3/4)<0 

Step by step solution :

Step  1  :

            3
 Simplify   —
            4

Equation at the end of step  1  :

          1                3
  ((0 -  (— • x)) -  8) -  —  < 0 
          4                4

Step  2  :

            1
 Simplify   —
            4

Equation at the end of step  2  :

          1                3
  ((0 -  (— • x)) -  8) -  —  < 0 
          4                4

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  4  as the denominator :

         8     8 • 4
    8 =  —  =  —————
         1       4  

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 - (8 • 4)     -x - 32
 ————————————  =  ———————
      4              4   

Equation at the end of step  3  :

  (-x - 32)    3
  ————————— -  —  < 0 
      4        4

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   -x - 32  =   -1 • (x + 32) 

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:

 (-x-32) - (3)     -x - 35
 —————————————  =  ———————
       4              4   

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -x - 35  =   -1 • (x + 35) 

Equation at the end of step  6  :

  -x - 35
  ———————  < 0 
     4   

Step  7  :

 7.1    Multiply both sides by  4 

 7.2    Multiply both sides by (-1)

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

      x+35  > 0

Solve Basic Inequality :

 7.3      Subtract  35  from both sides

            x > -35

Inequality Plot :

 7.4      Inequality plot for

         -0.250 x  - 8.750  <  0

  
 

One solution was found :