Linear Inequalities in One or Two Variables Flashcards

Which value of m does NOT satisfy 3m + 4 ≥ 2(m − 1)?

Answer: −7

3m + 4 ≥ 2m − 2 → m ≥ −6; m = −7 is less than −6, so it fails the inequality.

Solve for y: 4 − y/2 > 1

Answer: y < 6

−y/2 > −3 → y < 6 (multiply by −2, flip sign).

A company ships packages under 70 pounds. Each carton weighs 5 pounds and the contents weigh c pounds. If the total must be under 70 lb, which inequality is correct?

Answer: 5 + c < 70

Total weight is 5 + c, and it must be strictly less than 70, giving 5 + c < 70.

Solve the compound inequality: −1 ≤ (x + 3)/2 < 4

Answer: −5 ≤ x < 5

Multiply all parts by 2: −2 ≤ x + 3 < 8 → −5 ≤ x < 5.

Which region of the xy-plane satisfies both y ≥ x and y ≤ 4?

Answer: The area above y = x and at or below y = 4

y ≥ x is the region on or above the line y = x, and y ≤ 4 is at or below the horizontal line y = 4.

If 5a − 7 > 13 and 2a ≤ 10, how many integers satisfy both inequalities?

Answer: 1

5a > 20 → a > 4; 2a ≤ 10 → a ≤ 5; integers in (4, 5] are just {5} — one integer.

A photographer charges $50 for a session plus $10 per edited photo. A client's budget is at most $150. Which inequality shows the maximum number of edited photos n?

Answer: 50 + 10n ≤ 150

Total cost 50 + 10n must be at most 150, giving 50 + 10n ≤ 150 → n ≤ 10.

For what values of x does 2x + 3 > 7 AND x − 1 < 4 both hold?

Answer: 2 < x < 5

2x + 3 > 7 → x > 2; x − 1 < 4 → x < 5; combined: 2 < x < 5.