## Precalculus (6th Edition)

The equation is an identity. Every value of $x$ is a solution or the solution is $(-\infty,\infty)$
$\dfrac{1}{2}(6x+20)=x+4+2(x+3)$. 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.