The arithmetic mean of these five expressions is 24. What is the value of $x$? $$x + 8 \hspace{.5cm} 15 \hspace{.5cm} 2x \hspace{.5cm} 13 \hspace{.5cm} 2x + 4$$
To find the arithmetic mean of five expressions, I need to add them up and divide by five. I can write this as an equation: $\frac{x + 8 + 15 + 2x + 13 + 2x + 4}{5} = 24$. To solve for $x$, I need to isolate it on one side of the equation. First, I can simplify the numerator by combining like terms: $\frac{5x + 40}{5} = 24$. Next, I can multiply both sides by five to get rid of the fraction: $5x + 40 = 120$. Then, I can subtract 40 from both sides to get rid of the constant term: $5x = 80$. Finally, I can divide both sides by five to get the value of $x$: $x = 16$.

