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 $x$.

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