Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "/-2" was replaced by "/(-2)".

(2): ".5" was replaced by "(5/10)". 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/(-2)*(5/10))<0 

Step by step solution :

Step  1  :

            1
 Simplify   —
            2

Equation at the end of step  1  :

        16       m   1
  (0 -  ——) -  (—— • —)  < 0 
        10      -2   2

Step  2  :

             m
 Simplify   ——
            -2

Equation at the end of step  2  :

        16       m   1
  (0 -  ——) -  (—— • —)  < 0 
        10      -2   2

Step  3  :

            8
 Simplify   —
            5

Equation at the end of step  3  :

        8      m
  (0 -  —) -  ——  < 0 
        5     -4

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       -4 

      Least Common Multiple:
      20 

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 = 4

   Right_M = L.C.M / R_Deno = -5

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 • 4
   ——————————————————  =   ——————
         L.C.M               20  

   R. Mult. • R. Num.      m • -5
   ——————————————————  =   ——————
         L.C.M               20  

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 • 4 - (m • -5)     5m - 32
 —————————————————  =  ———————
        20               20   

Equation at the end of step  4  :

  5m - 32
  ———————  < 0 
    20   

Step  5  :

 5.1    Multiply both sides by  20 

 5.2    Divide both sides by  5  

      m-(32/5)  < 0

Solve Basic Inequality :

 5.3      Add  32/5  to both sides

             m < 32/5

Inequality Plot :

 5.4      Inequality plot for

         0.250 m  - 1.600  <  0

  
 

One solution was found :