1. The first problem asks to simplify the expression $9 - 6x - 42 + 4x - 45$. 2. To simplify, combine like terms. Like terms are terms that have the same variable raised to the same power. 3. Group the $x$ terms and the constant terms: $$-6x + 4x \quad \text{and} \quad 9 - 42 - 45$$ 4. Simplify each group: $$-6x + 4x = -2x$$ $$9 - 42 - 45 = 9 - 87 = -78$$ 5. Combine the simplified groups: $$-2x - 78$$ 6. Therefore, the simplified expression is $-2x - 78$, which corresponds to option D. --- 1. The second problem involves finding the perimeter of a triangle with sides $2x$, $2x - 4$, and $4x + 19$. 2. The perimeter $P$ of a triangle is the sum of the lengths of its sides: $$P = \text{side}_1 + \text{side}_2 + \text{side}_3$$ 3. Substitute the given side lengths and set equal to 79: $$2x + (2x - 4) + (4x + 19) = 79$$ 4. Combine like terms: $$2x + 2x - 4 + 4x + 19 = 79$$ $$8x + 15 = 79$$ 5. Solve for $x$: $$8x = 79 - 15$$ $$8x = 64$$ $$x = \frac{64}{8} = 8$$ 6. So, the value of $x$ is 8. Final answers: - Simplified expression: $-2x - 78$ - Value of $x$ in the triangle problem: $8$