Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.5" was replaced by "(25/10)". 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)-(m/(-(25/10)))<0 

Step by step solution :

Step  1  :

            5
 Simplify   —
            2

Equation at the end of step  1  :

        16     m5
  (0 -  ——) -  ——)  < 0 
        10     2 

Step  2  :

                -5
 Divide  m  by  ——
                2 

Equation at the end of step  2  :

        16     2m
  (0 -  ——) -  ——  < 0 
        10     -5

Step  3  :

            8
 Simplify   —
            5

Equation at the end of step  3  :

        8     2m
  (0 -  —) -  ——  < 0 
        5     -5

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       -5 

      Least Common Multiple:
      5 

Calculating Multipliers :

 4.2    Calculate multipliers for the two fractions


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = 1

   Right_M = L.C.M / R_Deno = -1

Making Equivalent Fractions :

 4.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)²   and  (y²+y)/(y+1)³  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

   L. Mult. • L. Num.      -8
   ——————————————————  =   ——
         L.C.M             5 

   R. Mult. • R. Num.      2m • -1
   ——————————————————  =   ———————
         L.C.M                5   

Adding fractions that have a common denominator :

 4.4       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:

 -8 - (2m • -1)     2m - 8
 ——————————————  =  ——————
       5              5   

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   2m - 8  =   2 • (m - 4) 

Equation at the end of step  5  :

  2 • (m - 4)
  ———————————  < 0 
       5     

Step  6  :

 6.1    Multiply both sides by  5 

 6.2    Divide both sides by  2 

Solve Basic Inequality :

 6.3      Add  4  to both sides

             m < 4

Inequality Plot :

 6.4      Inequality plot for

         0.400 X  - 1.600  <  0

  
 

One solution was found :