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 :

                     7*m+3/16-(3/5)<0 

Step by step solution :

Step  1  :

            3
 Simplify   —
            5

Equation at the end of step  1  :

          3     3
  (7m +  ——) -  —  < 0 
         16     5

Step  2  :

             3
 Simplify   ——
            16

Equation at the end of step  2  :

          3     3
  (7m +  ——) -  —  < 0 
         16     5

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  16  as the denominator :

           7m     7m • 16
     7m =  ——  =  ———————
           1        16   

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:

 7m • 16 + 3     112m + 3
 ———————————  =  ————————
     16             16   

Equation at the end of step  3  :

  (112m + 3)    3
  —————————— -  —  < 0 
      16        5

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       16 

      The right denominator is :       5 

      Least Common Multiple:
      80 

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 = 5

   Right_M = L.C.M / R_Deno = 16

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.      (112m+3) • 5
   ——————————————————  =   ————————————
         L.C.M                  80     

   R. Mult. • R. Num.      3 • 16
   ——————————————————  =   ——————
         L.C.M               80  

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (112m+3) • 5 - (3 • 16)     560m - 33
 ———————————————————————  =  —————————
           80                   80    

Equation at the end of step  4  :

  560m - 33
  —————————  < 0 
     80    

Step  5  :

 5.1    Multiply both sides by  80 

 5.2    Divide both sides by  560  

      m-(33/560)  < 0

Solve Basic Inequality :

 5.3      Add  33/560  to both sides

             m < 33/560

Inequality Plot :

 5.4      Inequality plot for

         7.000 m  - 0.412  <  0

  
 

One solution was found :