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Linear Inequalities in One or Two Variables Flashcards

7 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. Which of the following is a solution to −4x + 3 ≥ 11?

    Answer: x = −3

    −4x ≥ 8 → x ≤ −2; only x = −3 satisfies x ≤ −2.

  2. Solve for x: (x − 1)/2 < 4

    Answer: x < 9

    Multiply both sides by 2: x − 1 < 8; add 1: x < 9.

  3. Quality control requires a component to be between 4.95 cm and 5.05 cm, inclusive. Which inequality models acceptable length L?

    Answer: 4.95 ≤ L ≤ 5.05

    'Between ... inclusive' means both endpoints are included: 4.95 ≤ L ≤ 5.05.

  4. Which point is in the solution set of y < 2x + 1?

    Answer: (2, 4)

    Test (2, 4): 4 < 2(2)+1 = 5. True.

  5. Solve: −2 < 3x − 5 ≤ 7

    Answer: 1 < x ≤ 4

    Add 5 to all parts: 3 < 3x ≤ 12; divide by 3: 1 < x ≤ 4.

  6. A school bus holds at most 52 students. There are already 34 on board. Which inequality shows the number of additional students s that can board?

    Answer: s ≤ 18

    34 + s ≤ 52 → s ≤ 18.

  7. For which integer value of k is 5 ≤ 2k + 1 < 13 satisfied?

    Answer: k = 2

    Subtract 1: 4 ≤ 2k < 12; divide by 2: 2 ≤ k < 6; integers are 2, 3, 4, 5; k = 2 is the first listed.