SAT Math: Linear Inequalities Practice Questions
Practice solving linear inequalities, interpreting strict and inclusive boundaries, and checking points against constraints. Work each problem before opening its step-by-step explanation; every question is original and free to use without an account.
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1. Which inequality describes every solution of 5 - 2(3x - 1) < -3?
Explanation. Distribute to get 7 - 6x < -3. Subtract 7: -6x < -10. Dividing by -6 reverses the inequality, so x > 5/3. The endpoint is excluded because the original comparison is strict.
2. How many integer values of n satisfy -3 <= 2n + 1 < 8?
Explanation. Subtract 1 throughout: -4 <= 2n < 7. Divide by 2: -2 <= n < 7/2. The integers are -2, -1, 0, 1, 2, and 3, so there are 6.
3. A transit card costs $11. Each ride then costs $4. With a total budget of at most $47, what is the greatest whole number of rides that can be taken?
Explanation. For r rides, 11 + 4r <= 47, so 4r <= 36 and r <= 9. Nine rides use all $47; ten would exceed the budget.
4. Which point (x, y) satisfies y > -2x + 3?
Explanation. At (2, 0), the right side is -1 and 0 > -1. The points (0, 3) and (1, 1) lie on the excluded boundary; at (-1, 4), 4 is not greater than 5.
5. Which point satisfies all three conditions x >= 0, 3x + 2y <= 18, and x + y >= 7?
Explanation. At (4, 3), x is nonnegative, 3x + 2y = 18, and x + y = 7. The other points violate the second, third, and first condition respectively. Equality is allowed on both non-strict boundaries.
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