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Solution - Adding, subtracting and finding the least common multiple

x > \frac{140}{111}

x>140/111

Step by Step Solution

Rearrange:

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

x*(-37/12)-(-35/9)<0

Step by step solution :

Step 1 :

            35
 Simplify   ——
            9

Equation at the end of step 1 :

             37            35
  (x • (0 -  ——)) -  (0 -  ——)  < 0 
             12            9

Step 2 :

            37
 Simplify   ——
            12

Equation at the end of step 2 :

             37      -35
  (x • (0 -  ——)) -  ———  < 0 
             12       9

Step 3 :

Calculating the Least Common Multiple :

3.1    Find the Least Common Multiple

      The left denominator is :       12

      The right denominator is :       9

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
3	1	2	2
Product of all Prime Factors	12	9	36

Least Common Multiple:
36

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 = 3

   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.      -37x • 3
   ——————————————————  =   ————————
         L.C.M                36   

   R. Mult. • R. Num.      -35 • 4
   ——————————————————  =   ———————
         L.C.M               36

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:

 -37x • 3 - (-35 • 4)     140 - 111x
 ————————————————————  =  ——————————
          36                  36

Equation at the end of step 3 :

  140 - 111x
  ——————————  < 0 
      36

Step 4 :

4.1    Multiply both sides by 36

4.2    Multiply both sides by (-1)

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

      111x-140 > 0

4.3    Divide both sides by 111

      x-(140/111) > 0

Solve Basic Inequality :

 4.4      Add  140/111  to both sides

             x > 140/111

Inequality Plot :

 4.5      Inequality plot for

         -3.083 x  + 3.889  <  0

One solution was found :

x > 140/111

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