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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 for x: x/4 + 3 > 5

    Answer: x > 8

    x/4 > 2 → x > 8.

  2. Which inequality has x = −2 as its only integer solution between −5 and 0?

    Answer: −5 < 2x + 1 ≤ −3

    2(−2) + 1 = −3; for the range −5 −6 → x > −3, and 2x ≤ −4 → x ≤ −2; the only integer is x = −2.

  3. If 3 − 4x < −13, which of the following must be true?

    Answer: x > 4

    −4x 4 (dividing by −4 flips the sign).

  4. A bag can hold at most 20 kg. Books weigh 1.5 kg each and a laptop weighs 2 kg. If n books and 1 laptop are packed, which inequality applies?

    Answer: 1.5n + 2 ≤ 20

    Total weight is 1.5n + 2, and this must not exceed 20 kg, giving 1.5n + 2 ≤ 20.

  5. For the inequality 2y − x ≥ 6, which statement about the boundary line is correct?

    Answer: The boundary line y = (x + 6)/2 is solid

    Because ≥ includes equality, the boundary line is part of the solution and is drawn solid.

  6. Solve for x: −2x/5 ≥ 4

    Answer: x ≤ −10

    Multiply both sides by 5: −2x ≥ 20 → x ≤ −10 (dividing by −2 flips the sign).

  7. An elevator sign reads 'Maximum load: 1,200 lb.' Six people with an average weight of w pounds each are boarding. Which inequality is correct?

    Answer: 6w ≤ 1200

    The combined weight 6w must not exceed 1,200 lb, giving 6w ≤ 1,200.

  8. Which description correctly identifies all solutions to 3x + 1 > 2x − 5 AND x ≤ 3?

    Answer: −6 < x ≤ 3

    3x + 1 > 2x − 5 → x > −6; combined with x ≤ 3 gives −6 < x ≤ 3.