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Step by Step Solution

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "10.2" was replaced by "(102/10)".

Rearrange:

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

9/4-((102/10))<0

Step 1 :

            51
 Simplify   ——
            5

Equation at the end of step 1 :

  9    51
  — -  ——  < 0 
  4    5

Step 2 :

            9
 Simplify   —
            4

Equation at the end of step 2 :

  9    51
  — -  ——  < 0 
  4    5

Step 3 :

Calculating the Least Common Multiple :

3.1    Find the Least Common Multiple

      The left denominator is :       4

      The right denominator is :       5

Number of times each prime factor
appears in the factorization of:
Prime Factor	Left Denominator	Right Denominator	L.C.M = Max {Left,Right}
2	2	0	2
5	0	1	1
Product of all Prime Factors	4	5	20

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 = 5

   Right_M = L.C.M / R_Deno = 4

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.      9 • 5
   ——————————————————  =   —————
         L.C.M              20  

   R. Mult. • R. Num.      51 • 4
   ——————————————————  =   ——————
         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:

 9 • 5 - (51 • 4)     -159
 ————————————————  =  ————
        20             20

Equation at the end of step 3 :

  -159
  ————  < 0 
   20