#### Answer

The equation is an identity. Every value of $x$ is a solution or the solution is $(-\infty,\infty)$

#### Work Step by Step

$\dfrac{1}{2}(6x+20)=x+4+2(x+3)$.
Evaluate the products indicated on both sides of the equation:
$3x+10=x+4+2x+6$
Simplify the right side of the equation:
$3x+10=3x+10$
Take all terms with $x$ to the left side and all terms without $x$ to the right side:
$3x-3x=10-10$
$0=0$
Since both sides of the equation are the same, this is an identity and every value of $x$ is a solution.