Question

use distributive property and combining like terms to simplify each expression. easy to medium problems.

1. $-6(x + 2) - 2$
2. $4n - (7 - 6n)$
3. $-3 - 7(-3 - 6v)$
4. $-5(a - 6) + 2a$

Explanation:

Problem 9: $-6(x + 2) - 2$

Step 1: Apply Distributive Property

Multiply $-6$ with each term inside the parentheses: $-6(x) + (-6)(2) - 2 = -6x - 12 - 2$

Step 2: Combine Like Terms

Combine the constant terms: $-6x + (-12 - 2) = -6x - 14$

Step 1: Distribute the Negative Sign

Rewrite the expression as $4n - 7 + 6n$ (since $-(7 - 6n) = -7 + 6n$)

Step 2: Combine Like Terms

Combine the $n$ terms: $(4n + 6n) - 7 = 10n - 7$

Step 1: Apply Distributive Property

Multiply $-7$ with each term inside the parentheses: $-3 + 21 + 42v$ (since $-7(-3) = 21$ and $-7(-6v) = 42v$)

Step 2: Combine Like Terms

Combine the constant terms: $(-3 + 21) + 42v = 18 + 42v$

Answer:

$-6x - 14$

Problem 10: $4n - (7 - 6n)$