A point divides the segment joining A(2, 5) and B(9, -2) in the ratio 4 : 3. What is its $x$-coordinate?

$x=\frac{4\cdot 9+3\cdot 2}{4+3}=\frac{36+6}{7}=\frac{42}{7}=6$. The value 5 uses $m{x}_1+n{x}_2$, i.e. $m$ and $n$ swapped; 5.5 is the midpoint's $x$-coordinate, found by dropping the ratio altogether; 14 divides by $n=3$ instead of by $m+n=7$.