Solution - Adding, subtracting and finding the least common multiple

Rearrange:

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

                     -7/8-(m-13/8)≥0 

Step by step solution :

Step  1  :

            13
 Simplify   ——
            8 

Equation at the end of step  1  :

        7           13
  (0 -  —) -  (m -  ——)  ≥ 0 
        8           8 

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  8  as the denominator :

          m     m • 8
     m =  —  =  —————
          1       8  

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:

 m • 8 - (13)     8m - 13
 ————————————  =  ———————
      8              8   

Equation at the end of step  2  :

        7     (8m - 13)
  (0 -  —) -  —————————  ≥ 0 
        8         8    

Step  3  :

            7
 Simplify   —
            8

Equation at the end of step  3  :

        7     (8m - 13)
  (0 -  —) -  —————————  ≥ 0 
        8         8    

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:

 -7 - ((8m-13))     6 - 8m
 ——————————————  =  ——————
       8              8   

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   6 - 8m  =   -2 • (4m - 3) 

Equation at the end of step  5  :

  -2 • (4m - 3)
  —————————————  ≥ 0 
        8      

Step  6  :

 6.1    Multiply both sides by  8 

 6.2    Divide both sides by  -2 

Remember to flip the inequality sign:

 6.3    Divide both sides by  4  

      m-(3/4)  ≤ 0

Solve Basic Inequality :

 6.4      Add  3/4  to both sides

             m ≤ 3/4

Inequality Plot :

 6.5      Inequality plot for

         -X  + 0.750  ≤  0

  
 

One solution was found :