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bobbyet101
So it seems as if the first problem is asking this:

[tex]2 \frac{1}{6} - \frac{11}{15}x[/tex]. 

If x=0.15, then 11/15*(0.15) is 0.11 or 11/100. 

The second problem is asking:

[tex] \frac{x}{4} + \frac{1}{2} = \frac{x}{3} + \frac{1}{6} [/tex]

To solve algebraically, you want to get rid of the denominators under the x's. To do so, you want to multiply by the Least Common Multiple (LCM) of the denominators. For 3 and 4, the LCM is 12. Multiply everything by 12 to get:

3x+6=4x+2

Now, solve for x

Subtract 4x from both sides:
-x+6=2

Subtract 6 from both sides:
-x=-4

Multiply by -1 on both sides:
x=4. 

altavistard
Problem 1
We are to solve 2 1/6 - 11/15 x = 0.15   for x.
  Step 1:  Identify the LCD.  Taking the product of 6 and 15, we get the LCD 90.

Then 2 1/6 becomes 13/6, or 195/90, and - (11/15)x becomes -(66x/90).  We must also convert 0.15 to an improper fraction with denominator 90:

0.15(90)/90 = 13.5/90

Combine these two same-LCD fractions:  195/90 - 77x 

and equate this result, 195/90 - (66x)/90 = 13.5/90.

We can now eliminate the denominator, 90, from all three terms:

195 - 66x = 13.5

Let's elim. the decimal fraction; to do this, mult all three terms by 2:

390 - 132x = 27

Then 390-27= 132x   =>    363 = 132x

Dividing both sides by 132,     x = 363/132   (This can be reduced to

x = 11/4, or x = 2.75.

We must check this result.  Does 2 1/6 - (11/15)(2.75) = 0.15?

Does 13/6 -  121/60 = 0.15?

 Does 130/60 - 121/60 = 0.15?

   Does 9/60 = 0.15?   YES.  So the solution here is x = 2.75   or x= 11/4.


Next time, please post only ONE question at a time.
But for now, I will address your

Problem  #2:

Solve for x:   x/4 + 1/2 = x/3 + 1/6
1.  The LCD is 12.  Note that 12 is evenly divisible by 4, 2, 3 and 6.
2.  Multiplying all four terms by 12 allows us to write the equation as 

12(x/4) + 12(1/2) = 12(x/3) + 12/6

Simplifying, 3x + 6 = 4x + 2, which results in x = 4. 

Check:  If we subst. x =4, is x/4 + 1/2 = x/3 + 1/6 true?

   Is this true?  4/4 + 1/2 = 4/3 + 1/6

   Is 1 + 1/2 = 4/3 + 1/6?     Is 1 1/2 = 8/6 + 1/6?

Is 3/2 = 9/6?     Is 3/2 = 3/2?  YES.  So here, x =4 is a solution.

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