Find the coefficient of $x$ when $3(x - 4) + 4(7 - 2x^2 + 5x) - 8(2x - 1)$ is simplified.
I want to find the coefficient of $x$, which means I need to collect all the terms that have $x$ in them and add up their coefficients. To do that, I need to simplify the expression by using the distributive property and combining like terms. I'll start by distributing the 3, 4, and -8 to the parentheses: $3x - 12 + 28 - 8x^2 + 20x - 16x + 8$. Now I'll rearrange the terms so that the ones with the same degree of $x$ are together: $-8x^2 + 3x + 20x - 16x + 28 - 12 + 8$. Then I'll combine the like terms by adding or subtracting their coefficients: $-8x^2 + 7x + 24$. Now I can see that the coefficient of $x$ is 7, since it is the number that multiplies $x$. 