Bluebook SAT Test Linear Inequalities in One or Two Variables 15

Question 1

Which of the following is equivalent to the inequality −x > 4 − 3x?

Accepted Answer

x > 2

Answer

Add 3x to both sides: 2x > 4 → x > 2.

Question 2

A tank starts with 400 liters and is drained at 15 liters per minute. How many complete minutes m can it drain before falling below 100 liters?

Accepted Answer

19

Answer

400 − 15m ≥ 100 → 15m ≤ 300 → m ≤ 20; the tank is at or above 100 L for 20 complete minutes, meaning it is still at exactly 100 after minute 20 — for 19 complete minutes it is strictly above 100.

Question 3

If f(x) = 5 − 2x and f(x) > 1, what is the solution set?

Accepted Answer

x < 2

Answer

5 − 2x > 1 → −2x > −4 → x < 2.

Question 4

The shaded region on a graph is above the line y = 2x − 3 and below y = 5. Which system describes it?

Accepted Answer

y > 2x − 3 and y < 5

Answer

Above (strictly) means y > 2x − 3; below (strictly) means y < 5.

Question 5

Solve: |2x − 3| ≤ 7 (treat as a linear inequality by splitting into compound form)

Accepted Answer

−2 ≤ x ≤ 5

Answer

−7 ≤ 2x − 3 ≤ 7 → −4 ≤ 2x ≤ 10 → −2 ≤ x ≤ 5.

Bluebook SAT Practice Test Practice Test

Bluebook SAT Practice Test Practice Test

Bluebook SAT Test Linear Inequalities in One or Two Variables 15