So it seems as if the first problem is asking this:
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If x=0.15, then 11/15*(0.15) is 0.11 or 11/100.
The second problem is asking:
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:
Problem 1 We are to solve <span>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: </span><span>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 </span><span>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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