Mathematical Reasoning Algebra and Functions 1 Flashcards

Solve for x: 2x + 9 = 25

Answer: x = 8

Subtract 9 from both sides to get 2x = 16, then divide both sides by 2 to get x = 8.

What is the slope of the line represented by the equation 3x − 6y = 12?

Answer: 1/2

Rewrite in slope-intercept form: −6y = −3x + 12, so y = (1/2)x − 2. The coefficient of x is the slope, which is 1/2.

Factor the expression completely: x² − 9

Answer: (x + 3)(x − 3)

x² − 9 is a difference of squares (a² − b² = (a+b)(a−b)), where a = x and b = 3, giving (x + 3)(x − 3).

If g(x) = 3x² − 2x + 1, what is g(−1)?

Answer: 6

Substitute −1 for x: g(−1) = 3(−1)² − 2(−1) + 1 = 3(1) + 2 + 1 = 6.

Which value of x satisfies the inequality 2x − 5 > 7?

Answer: x = 7

Add 5 to both sides: 2x > 12, then divide by 2: x > 6. Only x = 7 is greater than 6.

A line passes through the points (2, 5) and (4, 9). What is the slope of the line?

Answer: 2

Use the slope formula m = (y₂ − y₁)/(x₂ − x₁) = (9 − 5)/(4 − 2) = 4/2 = 2.