Solve for \( x \).

[tex]\[ 3x = 6x - 2 \][/tex]




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Classwork 17

[tex]\[ \frac{1}{x} - 2x + y + \frac{1}{y + 2} \][/tex]



Answer :

Sure! Let's break down the given expression and simplify it step by step:

The given expression is:
[tex]\[ \frac{1}{xy} - 2x + y + \frac{\text{correction}}{y+2} \][/tex]

Let's analyze each term separately:

1. The first term:
[tex]\[ \frac{1}{xy} \][/tex]
This term is already in its simplest form.

2. The second term:
[tex]\[ -2x \][/tex]
This term is also in its simplest form and represents a linear expression in \(x\).

3. The third term:
[tex]\[ y \][/tex]
This term is a simple linear expression in \(y\).

4. The fourth term:
[tex]\[ \frac{\text{correction}}{y+2} \][/tex]
This term represents a fraction where "correction" is divided by \(y + 2\).

Now, let's combine all these simplified parts into a single expression, maintaining the order of operations:

[tex]\[ \frac{1}{xy} - 2x + y + \frac{\text{correction}}{y+2} \][/tex]

This should be the simplified form of the expression in question:

[tex]\[ \frac{\text{correction}}{y+2} - 2x + y + \frac{1}{xy} \][/tex]

Thus, the final simplified expression is:
[tex]\[ \frac{\text{correction}}{y+2} - 2x + y + \frac{1}{xy} \][/tex]

Answer:

x = 2/3

Step-by-step explanation:

3x = 6x - 2

-3x = -2

x = 2/3