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We substitute $3$ for $x$ in the equation. If the left- and right-hand sides are equal, then $x=3$ is a solution.
$17 + 5x = 47 - 4x - 3$
$17 + 5 \cdot {\color{#0000FF}{3}} \stackrel{?}{=} 47 - 4 \cdot {\color{#0000FF}{3}} - 3$
$17 + 15 \stackrel{?}{=} 47 - 12 - 3$
$32 =32$
Both sides of the equation are equal to $32.$ Thus, $x=3$ solves the equation.