Algebraic Concepts and Equations Flashcards

Factor the expression x² - 9 completely.

Answer: (x + 3)(x - 3)

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

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

Answer: x < -3

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

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

Answer: x = 5, y = 2

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

Which value of x satisfies x² = 81?

Answer: x = 9 or x = -9

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

Simplify: (3x²)(4x³)

Answer: 12x⁵

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

If a train travels at rate r mph for t hours, which expression gives the distance traveled?

Answer: r × t

Distance = rate × time, so distance = r × t.

What is the y-intercept of the equation 3x - 2y = 12?

Answer: y = -6

Set x = 0: -2y = 12, so y = -6.