The problem you uploaded asks to find $x$ given the following equations:

• $AB = 2x - 14$
• $AC = 9$
• $BC = x - 7$

The relationship between these segments suggests that point $C$ is between points $A$ and $B$, so:

$AB = AC + BC$

Substitute the given expressions for $AB$, $AC$, and $BC$:

$2x - 14 = 9 + (x - 7)$

Now, simplify and solve for $x$:

$2x - 14 = 9 + x - 7$ $2x - 14 = x + 2$ $2x - x = 2 + 14$ $x = 16$

Now that we have $x = 16$, let’s verify by plugging it back into the original segment equations to check if everything adds up:

• $AB = 2(16) - 14 = 32 - 14 = 18$
• $BC = 16 - 7 = 9$
• $AC = 9$

So, $AB = AC + BC = 9 + 9 = 18$, which is correct.

However, the choices provided were A) 2, B) 9, C) 10, D) 11, none of which is correct. The solution to the equation yields $x = 16$.

Would you like further clarification or details on this solution?

Here are 5 related questions you might explore:

1. What if the relationship between segments was different, e.g., $AC = AB + BC$?
2. How would you solve if both $AB$ and $BC$ were quadratic expressions?
3. Can you solve for other unknowns in triangle problems using segment relationships?
4. How does changing the position of point $C$ on the segment affect the result for $x$?
5. What geometric theorems can help in problems involving collinear points?

Tip: Always verify your solutions by substituting the result back into the original equations to check for consistency.