In this problem, we are given a line segment $FH$, where the total length is $FH = 11$. The segment is divided into two parts:

• $FG = 7$
• $GH = x + 1$

We need to solve for $x$ and find the length of $GH$.

Step 1: Set up the equation

Since the total length of $FH$ is 11, the sum of $FG$ and $GH$ should equal 11: $FG + GH = FH$ Substitute the known values: $7 + (x + 1) = 11$

Step 2: Solve for $x$

Simplify the equation: $7 + x + 1 = 11$ $x + 8 = 11$ Subtract 8 from both sides: $x = 3$

Step 3: Find $GH$

Now that we know $x = 3$, substitute it back into the expression for $GH$: $GH = x + 1 = 3 + 1 = 4$

Final Answer:

• $x = 3$
• $GH = 4$

Would you like more details on any step? Here are some related questions:

1. How would the equation change if $FH$ had a different length?
2. What is the general formula for finding $GH$ if $FG$ and $FH$ were unknown?
3. How would this problem change if $G$ were not exactly between $F$ and $H$?
4. What would happen if the segments included variables for both $FG$ and $GH$?
5. How can we verify the solution using different methods?

Tip: Always double-check your work by adding up the parts of the segment to ensure they match the total length!