Question 1: Expand the expression: -3(x + 4).

Answer: -3x - 12

Question 2: Simplify the expansion: -2(2x - 5).

Answer: -4x + 10

Question 3: Calculate the expanded form of: -5(3x + 2).

Answer: -15x - 10

Question 4: Expand and simplify: -4(x - 3).

Answer: -4x + 12

Question 5: Expand: -7(2x + 5).

Answer: -14x - 35

Question 6: Construct a problem where expanding -2(x + 6) results in -2x - 12. Write the original expression and verify your expansion.

Answer: Original expression: -2(x + 6). Expansion: -2x - 12.

Question 7: A rectangular garden's length is represented by 3x meters. Its width is given by -x + 4 meters. Write an expression for the perimeter, then expand and simplify it.

Answer: Perimeter: 2(3x + (-x + 4)) = 6x - 2x + 8 = 4x + 8.

Question 8: Find the expansion of: -6(2x - 3) and identify the coefficient of x.

Answer: -12x + 18; Coefficient of x is -12.

Question 9: Explain why expanding -3(x + 2) results in a negative coefficient for x. Provide a brief reasoning.

Answer: Because the -3 distributes to both x and 2, giving -3x and -6, making the x term negative.

Question 10: Solve the equation: -4(2x - 5) = 0 for x.

Answer: x = 5/2

Question 11: Identify and correct the mistake: Expand -2(x - 3) as -2x + 3.

Answer: Incorrect; the correct expansion is -2x + 6 because -2 distributes to both x and -3.