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 :

                     1/2*x-1/4-(5/8)<0 

Step by step solution :

Step  1  :

            5
 Simplify   —
            8

Equation at the end of step  1  :

    1         1     5
  ((— • x) -  —) -  —  < 0 
    2         4     8

Step  2  :

            1
 Simplify   —
            4

Equation at the end of step  2  :

    1         1     5
  ((— • x) -  —) -  —  < 0 
    2         4     8

Step  3  :

            1
 Simplify   —
            2

Equation at the end of step  3  :

    1         1     5
  ((— • x) -  —) -  —  < 0 
    2         4     8

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       4 

      Least Common Multiple:
      4 

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 = 2

   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.      x • 2
   ——————————————————  =   —————
         L.C.M               4  

   R. Mult. • R. Num.      1
   ——————————————————  =   —
         L.C.M             4

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:

 x • 2 - (1)     2x - 1
 ———————————  =  ——————
      4            4   

Equation at the end of step  4  :

  (2x - 1)    5
  ———————— -  —  < 0 
     4        8

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       4 

      The right denominator is :       8 

      Least Common Multiple:
      8 

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 = 2

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      (2x-1) • 2
   ——————————————————  =   ——————————
         L.C.M                 8     

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

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions

 (2x-1) • 2 - (5)     4x - 7
 ————————————————  =  ——————
        8               8   

Equation at the end of step  5  :

  4x - 7
  ——————  < 0 
    8   

Step  6  :

 6.1    Multiply both sides by  8 

 6.2    Divide both sides by  4  

      x-(7/4)  < 0

Solve Basic Inequality :

 6.3      Add  7/4  to both sides

             x < 7/4

Inequality Plot :

 6.4      Inequality plot for

         0.500 x  - 0.875  <  0

  
 

One solution was found :