### Home > CCA > Chapter 9 > Lesson 9.3.1 > Problem 9-74

9-74.

Thui made the following hypotheses: 2

*n*− 1 < 5 and*n*+ 1 ≤ 2*n*. Which of the following conclusions can she make? Homework Help ✎*n*≥ 1 and*n*≤ 3*n*≥ 1 and*n*< 3*n*> 1 and*n*≤ 3*n*> 1 and*n*< 3

Find the boundary points of the two equations.

2*n* − 1 = 5 *n* + 1 = 2*n*

2*n* = 6 1 = *n*

*n* = 3

Boundary points = 3 and 1

Test numbers on all sides of the boundary points.

Test *n* = 0

2(0) −1 < 5 0 +1 ≤ 2(0)

−1 < 5 1 ≤ 0

True False

Test *n* = 2

2(2) −1 < 5 2 +1 ≤ 2(2)

3 < 5 3 ≤ 4

True True

Test *n* = 4

2(4) +1 < 5 4 + 1 ≤ 2(4)

9 < 5 5 ≤ 8

False True

Because *n* = 2 is the only test that makes both equations true, (b), or 1 ≤ *n* < 3 is the correct answer.