If EF = 3x, FG = x + 3, and EG = 7, what is EF?


Given the points \( E \), \( F \), and \( G \) on a line segment, with:

- \( EF = 3x \)
- \( FG = x + 3 \)
- \( EG = 7 \)

We can use the segment addition postulate, which states that if point \( F \) lies between points \( E \) and \( G \), then:

\[
EF + FG = EG
\]

Substituting the given values:

\[
3x + (x + 3) = 7
\]

Simplify the equation:

\[
3x + x + 3 = 7
\]

\[
4x + 3 = 7
\]

Now, solve for \( x \):

\[
4x = 7 - 3
\]

\[
4x = 4
\]

\[
x = 1
\]

Now that we have \( x \), we can find the length of \( EF \):

\[
EF = 3x = 3(1) = 3
\]

Thus, \( EF = 3 \).

Would you like any further details or have any other questions?

Here are some related questions to consider:
1. How can you apply the segment addition postulate in other geometric problems?
2. What would change if \( FG \) were a different expression, like \( 2x + 5 \)?
3. How can you verify if point \( F \) lies between points \( E \) and \( G \)?
4. What if \( EG \) were not equal to 7, but a different number?
5. Can you solve for other segments if \( EF \) is known?
6. How do linear equations apply to segment lengths in geometry?
7. What happens if \( x \) results in a negative value?
8. How would this problem change if it involved a triangle instead of a line segment?

**Tip:** Always ensure that the relationships between the segment lengths make sense with respect to their positions on the line. This helps avoid errors in applying the segment addition postulate.

Learn how to solve a geometry problem involving segment lengths EF, FG, and EG using the Segment Addition Postulate. Follow a step-by-step solution process to determine the length of EF based on given equations and relationships between points E, F, and G. Suitable for high school students studying geometry.

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