Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.3" was replaced by "(23/10)".

Rearrange:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

                     -(23/10)-(j/4)<0 

Step by step solution :

Step  1  :

            j
 Simplify   —
            4

Equation at the end of step  1  :

        23     j
  (0 -  ——) -  —  < 0 
        10     4

Step  2  :

            23
 Simplify   ——
            10

Equation at the end of step  2  :

        23     j
  (0 -  ——) -  —  < 0 
        10     4

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       4 

      Least Common Multiple:
      20 

Calculating Multipliers :

 3.2    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 = 5

Making Equivalent Fractions :

 3.3      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.      -23 • 2
   ——————————————————  =   ———————
         L.C.M               20   

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

Adding fractions that have a common denominator :

 3.4       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:

 -23 • 2 - (j • 5)     -5j - 46
 —————————————————  =  ————————
        20                20   

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   -5j - 46  =   -1 • (5j + 46) 

Equation at the end of step  4  :

  -5j - 46
  ————————  < 0 
     20   

Step  5  :

 5.1    Multiply both sides by  20 

 5.2    Multiply both sides by (-1)

Flip the inequality sign since you are multiplying by a negative number

      5j+46  > 0

 5.3    Divide both sides by  5  

      j+(46/5)  > 0

Solve Basic Inequality :

 5.4      Subtract  46/5  from both sides

            j > -46/5

Inequality Plot :

 5.5      Inequality plot for

         -0.250 j  - 2.300  <  0

  
 

One solution was found :