Bluebook SAT Test Linear Inequalities in One or Two Variables 11

Question 1

If 6x − 5 ≤ 4x + 7, what is the largest integer value of x?

Accepted Answer

6

Answer

6x − 5 ≤ 4x + 7 → 2x ≤ 12 → x ≤ 6; the largest integer is 6.

Question 2

Carlos earns $15 per hour. He needs to earn more than $200 before the weekend. Which inequality shows how many hours h he must work?

Accepted Answer

15h > 200

Answer

He needs to earn more than $200, so 15h > 200, giving h > 13.33.

Question 3

Which system of inequalities is satisfied by (3, −1)?

Accepted Answer

y < x − 3 and y > −2

Answer

At (3, −1): y < 3 − 3 = 0 ✓ and y > −2 ✓; the other systems fail at least one inequality.

Question 4

Solve for x: 5(x − 2) < 3(x + 4)

Accepted Answer

x < 11

Answer

5x − 10 < 3x + 12 → 2x < 22 → x < 11.

Question 5

The temperature in a lab must stay strictly between 18°C and 26°C. Which compound inequality describes acceptable temperature T?

Accepted Answer

18 < T < 26

Answer

Strictly between means neither endpoint is included, so 18 < T < 26 is correct.

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