$$\frac { 1 } { 2 } ( 4 x + 6 ) = \frac { 1 } { 3 } ( 9 x - 24 )$$
$x=11$
$$\frac{1}{2}\times 4x+\frac{1}{2}\times 6=\frac{1}{3}\left(9x-24\right)$$
$$\frac{4}{2}x+\frac{1}{2}\times 6=\frac{1}{3}\left(9x-24\right)$$
$$2x+\frac{1}{2}\times 6=\frac{1}{3}\left(9x-24\right)$$
$$2x+\frac{6}{2}=\frac{1}{3}\left(9x-24\right)$$
$$2x+3=\frac{1}{3}\left(9x-24\right)$$
$$2x+3=\frac{1}{3}\times 9x+\frac{1}{3}\left(-24\right)$$
$$2x+3=\frac{9}{3}x+\frac{1}{3}\left(-24\right)$$
$$2x+3=3x+\frac{1}{3}\left(-24\right)$$
$$2x+3=3x+\frac{-24}{3}$$
$$2x+3=3x-8$$
$$2x+3-3x=-8$$
$$-x+3=-8$$
$$-x=-8-3$$
$$-x=-11$$
$$x=11$$
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