$$x+7=\frac{8x}{3}-\frac{17}{6}\frac{.5x}{2}$$
$x = \frac{168}{23} = 7\frac{7}{23} \approx 7.304347826$
$$6x+42=2\times 8x-\frac{17}{2}\times 0.5x$$
$$6x+42=16x-\frac{17}{2}\times 0.5x$$
$$6x+42=16x-\frac{17}{2}\times \frac{1}{2}x$$
$$6x+42=16x-\frac{17\times 1}{2\times 2}x$$
$$6x+42=16x-\frac{17}{4}x$$
$$6x+42=\frac{47}{4}x$$
$$6x+42-\frac{47}{4}x=0$$
$$-\frac{23}{4}x+42=0$$
$$-\frac{23}{4}x=-42$$
$$x=-42\left(-\frac{4}{23}\right)$$
$$x=\frac{-42\left(-4\right)}{23}$$
$$x=\frac{168}{23}$$
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