EDPT Algebraic Concepts and Equations 3

Question 1

Factor the expression x² - 9 completely.

Accepted Answer

(x + 3)(x - 3)

Answer

x² - 9 is a difference of squares, factoring as (x + 3)(x - 3).

Question 2

If 5 - 2x > 11, which of the following must be true?

Accepted Answer

x < -3

Answer

Subtract 5 from both sides: -2x > 6; dividing by -2 (flip sign) gives x < -3.

Question 3

What is the solution to the system: x + y = 7 and x - y = 3?

Accepted Answer

x = 5, y = 2

Answer

Adding both equations gives 2x = 10, so x = 5; substituting gives y = 2.

Question 4

Which value of x satisfies x² = 81?

Accepted Answer

x = 9 or x = -9

Answer

Both 9² = 81 and (-9)² = 81, so x = ±9.

Question 5

Simplify: (3x²)(4x³)

Accepted Answer

12x⁵

Answer

Multiply coefficients (3 × 4 = 12) and add exponents (2 + 3 = 5) to get 12x⁵.

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