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Solution - Adding, subtracting and finding the least common multiple

b < \frac{867}{25}

b<867/25

Step by Step Solution

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3.4" was replaced by "(34/10)". 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 :

(102/10)-(b/(34/10))>0

Step by step solution :

Step 1 :

            17
 Simplify   ——
            5

Equation at the end of step 1 :

  102    17
  ——— -  ——  > 0 
  10     5

Step 2 :

                17
 Divide  b  by  ——
                5

Equation at the end of step 2 :

  102    5b
  ——— -  ——  > 0 
  10     17

Step 3 :

            51
 Simplify   ——
            5

Equation at the end of step 3 :

  51    5b
  —— -  ——  > 0 
  5     17

Step 4 :

Calculating the Least Common Multiple :

4.1    Find the Least Common Multiple

      The left denominator is :       5

      The right denominator is :       17

Number of times each prime factor
appears in the factorization of:
Prime Factor	Left Denominator	Right Denominator	L.C.M = Max {Left,Right}
5	1	0	1
17	0	1	1
Product of all Prime Factors	5	17	85

Least Common Multiple:
85

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 = 17

   Right_M = L.C.M / R_Deno = 5

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.      51 • 17
   ——————————————————  =   ———————
         L.C.M               85   

   R. Mult. • R. Num.      5b • 5
   ——————————————————  =   ——————
         L.C.M               85

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:

 51 • 17 - (5b • 5)     867 - 25b
 ——————————————————  =  —————————
         85                85

Equation at the end of step 4 :

  867 - 25b
  —————————  > 0 
     85

Step 5 :

5.1    Multiply both sides by 85

5.2    Multiply both sides by (-1)

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

      25b-867 < 0

5.3    Divide both sides by 25

      b-(867/25) < 0

Solve Basic Inequality :

 5.4      Add  867/25  to both sides

             b < 867/25

Inequality Plot :

 5.5      Inequality plot for

         -0.294 b  + 10.200  >  0

One solution was found :

b < 867/25

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