Given the following equation, what is the value of $2x+1$?

$$6x+3=16$$

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Solve for $x$

$$6x+3=16$$ $$6x=13$$ $$x=\frac{13}{6}$$

Substitute the value of $x$ into $2x+1$.

$$2 \left(\frac{13}{6}\right)+1$$ $$\frac{13}{3}+1$$ $$\frac{13}{3}+\frac{3}{3}$$ $$\frac{16}{3}$$

Recognize that $6x+3$ is simply $2x+1$ tripled. You could also factor to come up with a similar conclusion.

$$6x+3=16$$ $$3(2x+1)=16$$

We can simply divide by $3$ on both sides to isolate $2x+1$.

$$2x+1=\frac{16}{3}$$