Bluebook SAT Test Linear Inequalities in One or Two Variables 3

Question 1

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

Accepted Answer

x = −3

Answer

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

Question 2

Solve for x: (x − 1)/2 < 4

Accepted Answer

x < 9

Answer

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

Question 3

Quality control requires a component to be between 4.95 cm and 5.05 cm, inclusive. Which inequality models acceptable length L?

Accepted Answer

4.95 ≤ L ≤ 5.05

Answer

'Between ... inclusive' means both endpoints are included: 4.95 ≤ L ≤ 5.05.

Question 4

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

Accepted Answer

(2, 4)

Answer

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

Question 5

Solve: −2 < 3x − 5 ≤ 7

Accepted Answer

1 < x ≤ 4

Answer

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

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