Linear Inequalities in One or Two Variables Flashcards

Solve for x: x/4 + 3 > 5

Answer: x > 8

x/4 > 2 → x > 8.

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.

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

Answer: x > 4

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

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.

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.

Solve for x: −2x/5 ≥ 4

Answer: x ≤ −10

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

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.

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.