Linear Inequalities in One or Two Variables Flashcards

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.

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.

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.

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.

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.

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.

Solve: −(x + 4) ≥ 2x − 1

Answer: x ≤ −1

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

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.