1. The problem is to simplify the algebraic expression $x + 6 + 3(x + 4)$. 2. Use the distributive property: $a(b + c) = ab + ac$. Here, distribute $3$ over $(x + 4)$: $$x + 6 + 3x + 12$$ 3. Combine like terms: $x + 3x = 4x$ and $6 + 12 = 18$. $$4x + 18$$ This is the simplified form of the first expression. 1. The second expression is $x + 9(x + 4)$. 2. Distribute $9$ over $(x + 4)$: $$x + 9x + 36$$ 3. Combine like terms: $x + 9x = 10x$. $$10x + 36$$ This matches the simplification given. 1. The third expression is $x + 8 + 5(x - 4)$. 2. Distribute $5$ over $(x - 4)$: $$x + 8 + 5x - 20$$ 3. Combine like terms: $x + 5x = 6x$ and $8 - 20 = -12$. $$6x - 12$$ Note: The user's step shows $5x - 12$, but combining $x + 5x$ should be $6x$. So the correct simplification is $6x - 12$. 1. The fourth expression is $x + 3 + 7(x - 5)$. 2. Distribute $7$ over $(x - 5)$: $$x + 3 + 7x - 35$$ 3. Combine like terms: $x + 7x = 8x$ and $3 - 35 = -32$. $$8x - 32$$ Note: The user's step shows $8x - 2$, but $3 - 5$ is incorrect; it should be $3 - 35 = -32$. So the correct simplification is $8x - 32$. Summary: - First expression simplifies to $4x + 18$. - Second expression simplifies to $10x + 36$. - Third expression simplifies to $6x - 12$. - Fourth expression simplifies to $8x - 32$.