Answer
$g=\frac{10}{9}$ or $g=2$
Work Step by Step
$|10-7g|=2g$ implies $10-7g=2g\\10=9g\\g=\frac{10}{9}$ or $10-7g=-2g\\10=5g\\g=2$.
Here we have no extraneous solutions. Thus $g=\frac{10}{9}$ or $g=2$.
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