Bluebook SAT Test Linear Inequalities in One or Two Variables 13

Question 1

Solve: 3 − 2(x + 1) ≥ 5

Accepted Answer

x ≤ −2

Answer

3 − 2x − 2 ≥ 5 → 1 − 2x ≥ 5 → −2x ≥ 4 → x ≤ −2.

Question 2

The inequality 0.5x + 1 < 6 is equivalent to which of the following?

Accepted Answer

x < 10

Answer

0.5x < 5 → x < 10.

Question 3

Which of the following points satisfies x + 2y ≤ 8 but NOT x − y > 0?

Accepted Answer

(2, 3)

Answer

(2,3): 2 + 6 = 8 ≤ 8 ✓, but 2 − 3 = −1 which is NOT > 0 ✓ — both conditions met.

Question 4

If −3 ≤ 2x + 1 ≤ 9, what is the range of values for 4x + 2?

Accepted Answer

−6 ≤ 4x + 2 ≤ 18

Answer

4x + 2 = 2(2x + 1); multiply the entire inequality by 2: −6 ≤ 4x + 2 ≤ 18.

Question 5

A city bus can carry at most 60 passengers. There are currently p passengers seated and 12 people standing. Which inequality is correct?

Accepted Answer

p + 12 ≤ 60

Answer

Total passengers p + 12 must not exceed 60, so p + 12 ≤ 60.

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