Question: 12. Find MQ
P----------------M----------------O
4x - 1 12x - 17
A horizontal line segment is shown in the top-left/center area of the page, with point P on the left, point M in the middle, and point O on the right; the left segment is labeled "4x - 1" and the right segment is labeled "12x - 17".
1. **State the problem:** We are given a line segment with points P, M, and O in that order. The segment PM is labeled as $4x - 1$ and the segment MO is labeled as $12x - 17$. We need to find the length of segment MQ.
2. **Analyze the problem:** Since M is between P and O, the entire segment PO is the sum of PM and MO.
3. **Assumption:** The problem asks for MQ, but the points given are P, M, and O. Since Q is not shown, we assume Q coincides with O or is a typo. If MQ means MO, we can find MO by first finding $x$.
4. **Set up the equation:** If the entire segment PO is known or if PM and MO are parts of a segment, and if PM and MO are equal (common in such problems), then:
$$4x - 1 = 12x - 17$$
5. **Solve for $x$:**
$$4x - 1 = 12x - 17$$
$$4x - 1 - 12x = -17$$
$$-8x - 1 = -17$$
$$-8x = -17 + 1$$
$$-8x = -16$$
$$x = \frac{-16}{-8}$$
$$x = 2$$
6. **Find MO:** Substitute $x=2$ into $12x - 17$:
$$12(2) - 17 = 24 - 17 = 7$$
7. **Find PM:** Substitute $x=2$ into $4x - 1$:
$$4(2) - 1 = 8 - 1 = 7$$
8. **Conclusion:** Both PM and MO are 7 units long. If MQ means MO, then:
$$\boxed{7}$$
If MQ is a different segment, please clarify the position of Q.