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Linear Inequalities in One or Two Variables Flashcards

8 cards from real Bluebook SAT Test practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. Solve: 3 − 2(x + 1) ≥ 5

    Answer: x ≤ −2

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

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

    Answer: x < 10

    0.5x < 5 → x < 10.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.