SAT Math · Algebra
Linear inequalities in one or two variables practice questions
Each free question on this page comes with its answer and a full explanation, and each one is marked easy, medium or hard.
- Question 6 · easyWhich of the following is equivalent to -3x + 7 ≤ 22?
- Question 8 · hardFor x ≥ 0 and y ≥ 0 satisfying x + 3y ≤ 15 and 2x + y ≤ 10, what is the greatest possible value of 3x + 5y?
- Question 29 · mediumWhat is the solution set of the system x > -3, x ≤ 5, and 2x - 1 < 9?
- Question 30 · easyWhich statement is true about the graph of y ≤ 3x - 2?
- Question 31 · easyA parking garage charges a $5 base fee plus $2.50 for each hour parked. A customer wants to pay no more than $25 total. What is…
- Question 60 · mediumThe boundary lines of y ≥ 2x - 4 and y ≤ -x + k intersect at the point where x = 2. What is the value of k?
- Question 126 · easyAn elevator can carry at most 2,000 pounds. If the average person weighs 165 pounds, what is the maximum number of people who…
- Question 127 · mediumWhich inequality is equivalent to |x - 5| ≤ 3?
- Question 128 · mediumA region in the coordinate plane is defined by x ≥ 0, y ≥ 0, and x + y ≤ 10. Which statement must be true for every point (x, y)…
- Question 129 · mediumFor the system x > k and x < 10 to have at least one solution, k must be less than what value?
- Question 146 · mediumWhich of the following is equivalent to -2(x-3) > 10?
- Question 147 · hardFor x ≥ 0 and y ≥ 0 satisfying x + y ≥ 6 and 2x + y ≥ 10, what is the smallest possible value of 4x + 3y?
- Question 168 · easyWhich statement is true about the graph of y < 2x + 3?
- Question 186 · mediumA parking lot must hold no fewer than 50 cars and no more than 120 cars at any time. What is the width of the range of possible…
- Question 191 · mediumA thermostat is set so that the temperature T, in degrees Celsius, satisfies -5 ≤ T ≤ 30. If an additional rule requires T > 10,…
- Question 207 · easyWhich of the following is equivalent to -x/3 ≤ 4?
- Question 226 · easyA delivery van can carry at most 5,000 pounds. If each package weighs 210 pounds on average, what is the maximum number of…
- Question 227 · hardFor x ≥ 0 and y ≥ 0 satisfying x + 2y ≤ 12 and 3x + y ≤ 16, what is the greatest possible value of 2x + 3y?
- Question 230 · easyA moving truck rental costs no more than $150 per day. The base fee is $40, plus $22 per hour of use. What is the maximum number…
- Question 246 · easyWhich of the following is equivalent to -3x + 5 ≤ 20?
- Question 247 · hardFor x ≥ 0 and y ≥ 0 satisfying 2x + y ≤ 14 and x + 3y ≤ 17, what is the greatest possible value of 3x + 2y?
- Question 250 · mediumWhat is the smallest integer value of x that satisfies both x > -3 and 2x - 7 > 5?
- Question 265 · hardFor x ≥ 0 and y ≥ 0 satisfying x + y ≤ 8 and 3x + y ≤ 16, what is the greatest possible value of x + 2y?
- Question 271 · easyWhich statement is true about the graph of y ≥ -2x + 6?
- Question 287 · hardFor x ≥ 0 and y ≥ 0 satisfying x + 3y ≤ 17 and 2x + y ≤ 14, what is the greatest possible value of 4x + 3y?
- Question 291 · easyWhich of the following is equivalent to -4x + 9 ≥ 25?
- Question 308 · easyA shipping company charges no more than $80 per package. The base fee is $15, plus $6.50 per pound. What is the maximum whole…
- Question 322 · hardFor x + y ≤ 20 and x - y ≥ 4, what is the largest integer value of y for which a valid value of x exists?