Bluebook SAT Test Linear Inequalities in One or Two Variables 10

Question 1

If 4 ≤ 3x − 2 ≤ 13, what is one possible integer value of x?

Accepted Answer

3

Answer

Adding 2: 6 ≤ 3x ≤ 15 → 2 ≤ x ≤ 5; integers in this range include 2, 3, 4, 5. x = 3 qualifies.

Question 2

Which graph represents the solution of 2 − x > −3 on a number line?

Accepted Answer

Open circle at 5, shaded to the left

Answer

2 − x > −3 → −x > −5 → x < 5; plotted as an open circle at 5 with shading left.

Question 3

A gardener needs to fence a rectangular area with at most 80 feet of fencing. The width is fixed at 15 feet. Which inequality represents possible lengths L?

Accepted Answer

2L + 30 ≤ 80

Answer

Perimeter = 2L + 2(15) = 2L + 30; this must be ≤ 80, giving 2L + 30 ≤ 80.

Question 4

Which value of k makes the inequality 2k − 9 > k + 1 true?

Accepted Answer

11

Answer

2k − 9 > k + 1 → k > 10; only k = 11 satisfies this.

Question 5

How many positive integers satisfy 3x + 5 < 20?

Accepted Answer

4

Answer

3x < 15 → x < 5; positive integers less than 5 are 1, 2, 3, 4 — exactly 4 values.

Bluebook SAT Practice Test Practice Test

Bluebook SAT Practice Test Practice Test

Bluebook SAT Test Linear Inequalities in One or Two Variables 10