1. The problem is to verify if $x=\frac{2}{3}$ is a solution to the equation $p(x) = 2x + 3x + 4 = 0$. 2. First, simplify the expression for $p(x)$ by combining like terms: $$p(x) = 2x + 3x + 4 = 5x + 4.$$ 3. Substitute $x=\frac{2}{3}$ into the simplified expression: $$p\left(\frac{2}{3}\right) = 5\times \frac{2}{3} + 4 = \frac{10}{3} + 4 = \frac{10}{3} + \frac{12}{3} = \frac{22}{3}.$$ 4. Since $\frac{22}{3} \neq 0$, $x=\frac{2}{3}$ is not a solution to the equation $p(x) = 0$. 5. To find the actual solution, set: $$5x + 4 = 0,$$ then solve for $x$: $$5x = -4,$$ $$x = -\frac{4}{5}.$$ The solution to $p(x) = 0$ is $x = -\frac{4}{5}$, not $\frac{2}{3}$.