1. The problem states the polynomial equation $p(x) = 2x + 3x + 4 = 0$ and suggests checking if $x=\frac{2}{3}$ is a solution. 2. First, simplify the polynomial expression: $2x + 3x + 4 = (2+3)x + 4 = 5x + 4$. 3. Substitute $x = \frac{2}{3}$ into $5x + 4$: $$5\times\frac{2}{3} + 4 = \frac{10}{3} + 4 = \frac{10}{3} + \frac{12}{3} = \frac{22}{3}.$$ 4. Since $\frac{22}{3} \neq 0$, $x=\frac{2}{3}$ is not a solution to the equation. 5. To find the solution, solve $5x + 4 = 0$: $$5x = -4$$ $$x = -\frac{4}{5}.$$ 6. The solution to the equation $p(x) = 0$ is $x = -\frac{4}{5}$, not $\frac{2}{3}$.