Linear Inequalities in One or Two Variables Flashcards

If 6x − 5 ≤ 4x + 7, what is the largest integer value of x?

Answer: 6

6x − 5 ≤ 4x + 7 → 2x ≤ 12 → x ≤ 6; the largest integer is 6.

Carlos earns $15 per hour. He needs to earn more than $200 before the weekend. Which inequality shows how many hours h he must work?

Answer: 15h > 200

He needs to earn more than $200, so 15h > 200, giving h > 13.33.

Which system of inequalities is satisfied by (3, −1)?

Answer: y −2

At (3, −1): y −2 ✓; the other systems fail at least one inequality.

Solve for x: 5(x − 2) < 3(x + 4)

Answer: x < 11

5x − 10 < 3x + 12 → 2x < 22 → x < 11.

The temperature in a lab must stay strictly between 18°C and 26°C. Which compound inequality describes acceptable temperature T?

Answer: 18 < T < 26

Strictly between means neither endpoint is included, so 18 < T < 26 is correct.

Which of the following best represents all x such that both x > −4 and x ≤ 3?

Answer: −4 < x ≤ 3

x > −4 (open at −4) and x ≤ 3 (closed at 3) combine to −4 < x ≤ 3.

A chef needs at least 3 pounds of flour but cannot carry more than 8 pounds total of flour f and sugar s. Which represents these constraints?

Answer: f ≥ 3 and f + s ≤ 8

At least 3 lb of flour means f ≥ 3; cannot exceed 8 lb combined means f + s ≤ 8.

If 2 ≤ x ≤ 7, what is the maximum value of 3 − 2x?

Answer: −1

3 − 2x is a decreasing function of x; it is maximized at the smallest x = 2: 3 − 4 = −1.