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 :

                     -3/5*x+1/5-(7/20)>0 

Step by step solution :

Step  1  :

             7
 Simplify   ——
            20

Equation at the end of step  1  :

       3     1   7
  ((0-(—•x))+—)-——  > 0 
       5     5  20

Step  2  :

            1
 Simplify   —
            5

Equation at the end of step  2  :

          3          1      7
  ((0 -  (— • x)) +  —) -  ——  > 0 
          5          5     20

Step  3  :

            3
 Simplify   —
            5

Equation at the end of step  3  :

          3          1      7
  ((0 -  (— • x)) +  —) -  ——  > 0 
          5          5     20

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:

 -3x + 1     1 - 3x
 ———————  =  ——————
    5          5   

Equation at the end of step  4  :

  (1 - 3x)     7
  ———————— -  ——  > 0 
     5        20

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       20 

      Least Common Multiple:
      20 

Calculating Multipliers :

 5.2    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 = 1

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      (1-3x) • 4
   ——————————————————  =   ——————————
         L.C.M                 20    

   R. Mult. • R. Num.       7
   ——————————————————  =   ——
         L.C.M             20

Adding fractions that have a common denominator :

 5.4       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:

 (1-3x) • 4 - (7)     -12x - 3
 ————————————————  =  ————————
        20               20   

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -12x - 3  =   -3 • (4x + 1) 

Equation at the end of step  6  :

  -3 • (4x + 1)
  —————————————  > 0 
       20      

Step  7  :

 7.1    Multiply both sides by  20 

 7.2    Divide both sides by  -3 

Remember to flip the inequality sign:

 7.3    Divide both sides by  4  

      x+(1/4)  < 0

Solve Basic Inequality :

 7.4      Subtract  1/4  from both sides

            x < -1/4

Inequality Plot :

 7.5      Inequality plot for

         -0.600 X  - 0.150  <  0

  
 

One solution was found :