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Solution - Adding, subtracting and finding the least common multiple

x = - \frac{476}{165} = - 2.885

x=-476/165=-2.885

Step by Step Solution

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

17/15-(-11/28*x)=0

Step by step solution :

Step 1 :

            11
 Simplify   ——
            28

Equation at the end of step 1 :

  17           11
  —— -  (0 -  (—— • x))  = 0 
  15           28

Step 2 :

            17
 Simplify   ——
            15

Equation at the end of step 2 :

  17    -11x
  —— -  ————  = 0 
  15     28

Step 3 :

Calculating the Least Common Multiple :

3.1    Find the Least Common Multiple

      The left denominator is :       15

      The right denominator is :       28

Number of times each prime factor
appears in the factorization of:
Prime Factor	Left Denominator	Right Denominator	L.C.M = Max {Left,Right}
3	1	0	1
5	1	0	1
2	0	2	2
7	0	1	1
Product of all Prime Factors	15	28	420

Least Common Multiple:
420

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 = 28

   Right_M = L.C.M / R_Deno = 15

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.      17 • 28
   ——————————————————  =   ———————
         L.C.M               420  

   R. Mult. • R. Num.      -11x • 15
   ——————————————————  =   —————————
         L.C.M                420

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:

 17 • 28 - (-11x • 15)     165x + 476
 —————————————————————  =  ——————————
          420                 420

Equation at the end of step 3 :

  165x + 476
  ——————————  = 0 
     420

Step 4 :

When a fraction equals zero :

 4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

  165x+476
  ———————— • 420 = 0 • 420
    420

Now, on the left hand side, the 420 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
165x+476 = 0

Solving a Single Variable Equation :

4.2      Solve  :    165x+476 = 0

Subtract 476 from both sides of the equation :
                      165x = -476
Divide both sides of the equation by 165:
                     x = -476/165 = -2.885

One solution was found :

x = -476/165 = -2.885

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