Bluebook SAT Test Linear Inequalities in One or Two Variables 14

Question 1

Solve for x: x/4 + 3 > 5

Accepted Answer

x > 8

Answer

x/4 > 2 → x > 8.

Question 2

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

Accepted Answer

−5 < 2x + 1 ≤ −3

Answer

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

Question 3

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

Accepted Answer

x > 4

Answer

−4x < −16 → x > 4 (dividing by −4 flips the sign).

Question 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?

Accepted Answer

1.5n + 2 ≤ 20

Answer

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

Question 5

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

Accepted Answer

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

Answer

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

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