1. **State the problem:** Find the value of $x$ that satisfies the equation $$-8(x + 16) + 14x = -98.$$\n\n2. **Write the formula and rules:** We will use the distributive property to expand and then combine like terms. After that, isolate $x$ by performing inverse operations.\n\n3. **Expand the left side:** $$-8(x + 16) + 14x = -8x - 128 + 14x.$$\n\n4. **Combine like terms:** $$-8x + 14x - 128 = 6x - 128.$$\n\n5. **Rewrite the equation:** $$6x - 128 = -98.$$\n\n6. **Add 128 to both sides to isolate terms with $x$:** $$6x - 128 + 128 = -98 + 128,$$\n$$6x = 30.$$\n\n7. **Divide both sides by 6 to solve for $x$:** $$\cancel{6}x / \cancel{6} = 30 / 6,$$\n$$x = 5.$$\n\n**Final answer:** $x = 5$