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If UV = 3x, VW = x + 2, and UW = 10, what is UVSimplify your answer and write it as a proper fraction, mixed number, or integer.

We are given that \( UV = 3x \), \( VW = x + 2 \), and \( UW = 10 \). From the diagram, we can infer that \( UW \) is the total length of the segment, which is the sum of \( UV \) and \( VW \). Thus, we can set up the equation:

\[
UV + VW = UW
\]

Substitute the given expressions:

\[
3x + (x + 2) = 10
\]

Now, solve for \( x \):

\[
3x + x + 2 = 10
\]
\[
4x + 2 = 10
\]
\[
4x = 10 - 2
\]
\[
4x = 8
\]
\[
x = \frac{8}{4} = 2
\]

Now that we have \( x = 2 \), substitute it back into the expression for \( UV \):

\[
UV = 3x = 3(2) = 6
\]

Thus, \( UV = 6 \).

Let me know if you would like more details or have any questions. Here are some related questions for further exploration:

1. What is the value of \( VW \)?
2. How can you verify the total length of \( UW \) using the values of \( UV \) and \( VW \)?
3. If the total length \( UW \) was 15 instead of 10, how would the value of \( UV \) change?
4. How would the problem change if \( VW = 2x + 3 \)?
5. How can you use this type of linear equation problem in real-life scenarios?

**Tip:** Always verify your solution by substituting the value of the variable back into the original equation.

If UV = 3x, VW = x + 2, and UW = 10, what is UV? Simplify your answer and write it as a proper fraction, mixed number, or integer.

Learn how to solve for the segment UV in a linear equation with UV = 3x, VW = x + 2, and UW = 10. This problem covers algebraic concepts and geometric postulates, suitable for students in Grades 6-8.

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