first off, we'll convert the mixed fractions to "improper", and proceed,
[tex]\bf \stackrel{mixed}{2\frac{7}{9}}\implies \cfrac{2\cdot 9+7}{9}\implies \stackrel{improper}{\cfrac{25}{9}}
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\stackrel{mixed}{1\frac{x}{9}}\implies \cfrac{1\cdot 9+x}{9}\implies \stackrel{improper}{\cfrac{9+x}{9}}\\\\
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\cfrac{25}{9}=\cfrac{9+x}{9}\implies 25=9+x\implies 25-9=x\implies 16=x[/tex]
