Fill in the blanks with the appropriate sign

Explanation

Let's solve them:

1.  2(x + 4) = 2x + 8
   • Explanation: When you distribute the 2 to both terms inside the parentheses, you multiply each term by 2. So, 2 times x is 2x, and 2 times 4 is 8.
2. 2(x - 4) = 2x - 8
   • Explanation: Similar to the first equation, when you distribute the 2 to both terms inside the parentheses, you multiply each term by 2. So, 2 times x is 2x, and 2 times (-4) is -8.
3. -2(x + 4) = -2x - 8
   • Explanation: In this equation, you're not only distributing the -2 but also changing the sign of each term inside the parentheses. When you multiply -2 by x, you get -2x; when you multiply -2 by 4, you get -8.
4. -2(-x - 4) = 2x + 8
   • Explanation: Here, you're distributing -2 to both terms inside the parentheses and changing the sign of each term. When you multiply -2 by -x, you get 2x (because -2 • -x = 2x); when you multiply -2 by -4, you get +8 (because -2 • -4 = 8).

In all these equations, the distributive property is applied to multiply the number outside the parentheses with each term inside the parentheses. The sign changes occur as a result of multiplying by negative numbers, which is an essential aspect of the distributive property.