What is the \(x\)-coordinate of the \(x\)-intercept of the line \(\dfrac{4}{7}x+\dfrac{5}{6}y=3\)

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To find the \(x\)-intercept of an equation, simply set \(y=0\) and solve for \(x\).

$$ \frac{4}{7}x+\frac{5}{6}y=3 $$ $$ \frac{4}{7}x+\frac{5}{6}(0)=3 $$ $$ \frac{4}{7}x=3 $$ $$ x=3\left(\frac{7}{4}\right)$$ $$ x=\frac{21}{4} $$