Solve one-variable inequalities and identify the largest or smallest integer values that satisfy a given constraint.
60 original linear inequalities questions in the SAT Ranker bank, with instant scoring and an Elo-based rank once you sign up. Below are a few free samples with full explanations.
If 2x - 1 < 3, what is the largest integer value x can be?
Solving gives x < 2, and the inequality is strict, so x cannot equal 2. The answer is 1. 2 takes the boundary itself, but the inequality is strict so 2 is excluded; 3 moves off the boundary in the wrong direction; 4 stops after isolating 2x and never divides by 2.
If 4x - 3 < 37, what is the largest integer value x can be?
Solving gives x < 10, and the inequality is strict, so x cannot equal 10. The answer is 9. 10 takes the boundary itself, but the inequality is strict so 10 is excluded; 11 moves off the boundary in the wrong direction; 40 stops after isolating 4x and never divides by 4.
If 7x - 10 > 4, what is the smallest integer value x can be?
Solving gives x > 2, and the inequality is strict, so x cannot equal 2. The answer is 3. 2 takes the boundary itself, but the inequality is strict so 2 is excluded; 1 moves off the boundary in the wrong direction; 14 stops after isolating 7x and never divides by 7.
If 3x - 11 > -26, what is the smallest integer value x can be?
Solving gives x > -5, and the inequality is strict, so x cannot equal -5. The answer is -4. -5 takes the boundary itself, but the inequality is strict so -5 is excluded; -6 moves off the boundary in the wrong direction; -15 stops after isolating 3x and never divides by 3.
If 3x - 8 < -26, what is the largest integer value x can be?
Solving gives x < -6, and the inequality is strict, so x cannot equal -6. The answer is -7. -6 takes the boundary itself, but the inequality is strict so -6 is excluded; -5 moves off the boundary in the wrong direction; -18 stops after isolating 3x and never divides by 3.