Linear Inequalities in One or Two Variables Flashcards

Solve: 3 − 2(x + 1) ≥ 5

Answer: x ≤ −2

3 − 2x − 2 ≥ 5 → 1 − 2x ≥ 5 → −2x ≥ 4 → x ≤ −2.

The inequality 0.5x + 1 < 6 is equivalent to which of the following?

Answer: x < 10

0.5x < 5 → x < 10.

Which of the following points satisfies x + 2y ≤ 8 but NOT x − y > 0?

Answer: (2, 3)

(2,3): 2 + 6 = 8 ≤ 8 ✓, but 2 − 3 = −1 which is NOT > 0 ✓ — both conditions met.

If −3 ≤ 2x + 1 ≤ 9, what is the range of values for 4x + 2?

Answer: −6 ≤ 4x + 2 ≤ 18

4x + 2 = 2(2x + 1); multiply the entire inequality by 2: −6 ≤ 4x + 2 ≤ 18.

A city bus can carry at most 60 passengers. There are currently p passengers seated and 12 people standing. Which inequality is correct?

Answer: p + 12 ≤ 60

Total passengers p + 12 must not exceed 60, so p + 12 ≤ 60.

What is the greatest integer solution to 7x − 3 < 4x + 12?

Answer: 4

3x < 15 → x < 5; the greatest integer strictly less than 5 is 4.

Which ordered pair lies in the solution of the system: y x − 2?

Answer: (1, 2)

(1,2): 2 1−2=−1 ✓. All other choices fail at least one inequality.

Emma has $45 and earns $12 per hour babysitting. She wants at least $100 total. How many complete hours h must she work?

Answer: 5

45 + 12h ≥ 100 → 12h ≥ 55 → h ≥ 4.58; she must work at least 5 complete hours.