Linear Inequalities in One or Two Variables Flashcards

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

Answer: x = −3

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

Solve for x: (x − 1)/2 < 4

Answer: x < 9

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

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.

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

Answer: (2, 4)

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

Solve: −2 < 3x − 5 ≤ 7

Answer: 1 < x ≤ 4

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

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.

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.