Linear Inequalities in One or Two Variables Flashcards

Which of the following is in the solution set of both x > −2 and x ≤ 5?

Answer: x = 0

Need −2 < x ≤ 5; x = 0 satisfies both.

Solve for x: 5x − 8 < 3x + 4

Answer: x < 6

2x < 12 → x < 6.

A taxi driver wants to earn more than $120 in a shift at $3 per mile. He has driven 20 miles. How many more miles m must he drive?

Answer: m > 20

3(20 + m) > 120 → 60 + 3m > 120 → 3m > 60 → m > 20.

If −3 ≤ x ≤ 5, what is the greatest possible value of 2x − 1?

Answer: 9

Maximize by choosing x = 5: 2(5) − 1 = 9.

Which point is in the region defined by y > 2x − 3 AND y < −x + 6?

Answer: (1, 2)

Test (1, 2): 2 > −1 ✓; 2 < 5 ✓.

Solve for n: 3n + 4 > −8 AND 2n − 1 ≤ 5

Answer: Both A and B express the same solution

n > −4 and n ≤ 3; options A and B state the same solution in different notation.

Which value of t satisfies 2t + 1 ≥ 7 but NOT t − 3 > 4?

Answer: t = 3

2t ≥ 6 → t ≥ 3; t > 7 excluded; t = 3 satisfies t ≥ 3 and not t > 7.