Simplify limit as x approaches 2 of 2x+1

$lim_{x \to 2} 2 x + 1$

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $2$ .

$lim_{x \to 2} 2 x + lim_{x \to 2} 1$

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$2 lim_{x \to 2} x + lim_{x \to 2} 1$

Evaluate the limit of $1$ which is constant as $x$ approaches $2$ .

$2 lim_{x \to 2} x + 1$

Simplify terms.

Simplify each term.

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

$2 \cdot 2 + 1$

Multiply $2$ by $2$ .

$4 + 1$

Add $4$ and $1$ .

$5$