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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. If 4 ≤ 3x − 2 ≤ 13, what is one possible integer value of x?

    Answer: 3

    Adding 2: 6 ≤ 3x ≤ 15 → 2 ≤ x ≤ 5; integers in this range include 2, 3, 4, 5. x = 3 qualifies.

  2. Which graph represents the solution of 2 − x > −3 on a number line?

    Answer: Open circle at 5, shaded to the left

    2 − x > −3 → −x > −5 → x < 5; plotted as an open circle at 5 with shading left.

  3. A gardener needs to fence a rectangular area with at most 80 feet of fencing. The width is fixed at 15 feet. Which inequality represents possible lengths L?

    Answer: 2L + 30 ≤ 80

    Perimeter = 2L + 2(15) = 2L + 30; this must be ≤ 80, giving 2L + 30 ≤ 80.

  4. Which value of k makes the inequality 2k − 9 > k + 1 true?

    Answer: 11

    2k − 9 > k + 1 → k > 10; only k = 11 satisfies this.

  5. How many positive integers satisfy 3x + 5 < 20?

    Answer: 4

    3x < 15 → x < 5; positive integers less than 5 are 1, 2, 3, 4 — exactly 4 values.

  6. Which point is NOT in the solution region of y ≥ −x + 4?

    Answer: (0, 3)

    At (0, 3): y = 3 and −x + 4 = 4; since 3 < 4, the point is below the line and not in the solution region.

  7. Solve: −(x + 4) ≥ 2x − 1

    Answer: x ≤ −1

    Expanding: −x − 4 ≥ 2x − 1 → −3x ≥ 3 → x ≤ −1.

  8. A student needs to average at least 80 on three tests. The first two scores are 74 and 85. What is the minimum score s needed on the third test?

    Answer: 81

    (74 + 85 + s)/3 ≥ 80 → 159 + s ≥ 240 → s ≥ 81.