1. **State the problem:** We are given two functions $h(x) = -5x + 1$ and $g(x) = 2x^2$. We need to find the value of $h(7) - g(3)$. 2. **Recall the formulas:** - For $h(x)$, substitute $x$ with the given value and calculate. - For $g(x)$, substitute $x$ with the given value and calculate. 3. **Calculate $h(7)$:** $$h(7) = -5(7) + 1 = -35 + 1 = -34$$ 4. **Calculate $g(3)$:** $$g(3) = 2(3)^2 = 2(9) = 18$$ 5. **Find $h(7) - g(3)$:** $$h(7) - g(3) = -34 - 18 = -52$$ **Final answer:** $$\boxed{-52}$$