Linear Inequalities in One or Two Variables Flashcards

If 7 − 3x ≥ −2, which of the following is the solution set?

Answer: x ≤ 3

Subtracting 7 gives −3x ≥ −9, and dividing by −3 (flipping the sign) gives x ≤ 3.

A theater sells adult tickets for $12 and student tickets for $8. The drama club needs to raise at least $240. If they sell exactly 10 adult tickets, what is the minimum number of student tickets s they must sell?

Answer: 15

10(12) + 8s ≥ 240 → 120 + 8s ≥ 240 → 8s ≥ 120 → s ≥ 15.

Which of the following is a solution to the inequality −5x + 2 > 17?

Answer: x = −4

−5(−4) + 2 = 22 > 17 ✓; for all other choices the inequality fails.

On a number line, the inequality −4 < 2x ≤ 8 is represented by what interval?

Answer: (−2, 4]

Dividing every part by 2 gives −2 < x ≤ 4, which corresponds to the interval (−2, 4].

Alicia wants to keep her monthly phone bill under $60. Her plan charges $20 plus $0.08 per text. Which inequality gives the maximum number of texts t she can send?

Answer: 0.08t < 40

20 + 0.08t < 60 simplifies to 0.08t < 40, so t < 500.

Which ordered pair satisfies the inequality 3x − 2y > 6?

Answer: (4, 2)

3(4) − 2(2) = 8 > 6 ✓; the other choices yield 3, 3, and 6, which do not satisfy the strict inequality.

Solve for x: (2x + 1)/3 < 5

Answer: x < 7

Multiply both sides by 3: 2x + 1 < 15 → 2x < 14 → x < 7.

A warehouse can hold at most 500 boxes. There are already 185 boxes inside. A forklift loads b boxes at a time and makes at least 5 trips. Which inequality correctly models this situation?

Answer: 185 + 5b ≤ 500

After 5 trips, the total is 185 + 5b, and this must not exceed 500, giving 185 + 5b ≤ 500.