Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.5" was replaced by "(15/10)". 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 :

           (25/10)*m-(15/10)*(2-3*m)-(2*(m+1))>0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

    25     15
  ((——•m)-(——•(2-3m)))-2•(m+1)  > 0 
    10     10

Step  2  :

            3
 Simplify   —
            2

Equation at the end of step  2  :

    25     3
  ((——•m)-(—•(2-3m)))-2•(m+1)  > 0 
    10     2

Step  3  :

Equation at the end of step  3  :

    25    3•(2-3m)
  ((——•m)-————————)-2•(m+1)  > 0 
    10       2    

Step  4  :

            5
 Simplify   —
            2

Equation at the end of step  4  :

    5    3•(2-3m)
  ((—•m)-————————)-2•(m+1)  > 0 
    2       2    

Step  5  :

Adding fractions which have a common denominator :

 5.1       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:

 5m - (3 • (2-3m))     14m - 6
 —————————————————  =  ———————
         2                2   

Equation at the end of step  5  :

  (14m - 6)    
  ————————— -  2 • (m + 1)  > 0 
      2        

Step  6  :

Rewriting the whole as an Equivalent Fraction :

 6.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  2  as the denominator :

                   2 • (m + 1)     2 • (m + 1) • 2
    2 • (m + 1) =  ———————————  =  ———————————————
                        1                 2       

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

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   14m - 6  =   2 • (7m - 3) 

Adding fractions that have a common denominator :

 7.2       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-3) - (2 • (m+1))     5m - 5
 ————————————————————  =  ——————
          1                 1   

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   5m - 5  =   5 • (m - 1) 

Equation at the end of step  8  :

  5 • (m - 1)  > 0 

Step  9  :

 9.1    Divide both sides by  5 

Solve Basic Inequality :

 9.2      Add  1  to both sides

             m > 1

Inequality Plot :

 9.3      Inequality plot for

         5.000 X  - 5.000  >  0

  
 

One solution was found :