If EF = x + 1, FG = 5x − 2, and EG = 11, what is FG?


Given the problem where \( EF = x + 1 \), \( FG = 5x - 2 \), and \( EG = 11 \), we need to find the value of \( FG \).

Since \( E \), \( F \), and \( G \) lie on a straight line, the sum of the segments \( EF \) and \( FG \) should equal the total length \( EG \):

\[
EF + FG = EG
\]

Substituting the given expressions:

\[
(x + 1) + (5x - 2) = 11
\]

Now, combine like terms:

\[
6x - 1 = 11
\]

Next, add 1 to both sides:

\[
6x = 12
\]

Now, divide both sides by 6:

\[
x = 2
\]

Finally, substitute \( x = 2 \) into the expression for \( FG \):

\[
FG = 5x - 2 = 5(2) - 2 = 10 - 2 = 8
\]

So, \( FG = 8 \).

Would you like more details or have any questions? 

Here are some related questions for further practice:

1. If \( EF = 2x + 3 \) and \( EG = 15 \), what is \( FG \)?
2. If \( EF = x - 4 \) and \( FG = 3x + 1 \), find \( EG \) when \( x = 3 \).
3. If \( EF = 4x + 1 \) and \( FG = 2x - 3 \), find \( EG \) in terms of \( x \).
4. What would \( FG \) be if \( EG \) were 14 instead of 11?
5. If \( EF = x \), \( FG = 2x + 3 \), and \( EG = 19 \), solve for \( x \) and \( FG \).

**Tip:** When given segment lengths in algebraic form, always set up the equation based on the sum of the segments to find unknown variables easily.

Explore how to solve linear equations with unknown variables using a detailed example problem. This problem involves determining the value of FG given EF = x + 1, FG = 5x - 2, and EG = 11. Suitable for Grades 7-9 students studying algebraic equations and linear relationships.

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