Compound Inequalities Worksheets Grade 9

1. Olivia is a marine biologist monitoring the oxygen concentration (in mg/L) in a coastal estuary. The concentration C must satisfy two conditions to support aquatic life: it must be at least 20 mg/L, and it must be less than 50 mg/L. If the concentration is modeled by the expression 5x - 10, where x is the depth in meters, write and solve the compound inequality that represents all depths x for which the oxygen concentration meets both conditions.
2. Solve the compound inequality: 4x - 7 ≤ 9 and 2x + 5 > 11. What is the smallest integer value of x that satisfies both inequalities?
3. |2x - 5| + 3 ≥ 10 = ?

…and 4 more problems

1. A number line is drawn with points labeled at -10, 0, and 10. Two rays are shown: one starts at -3 and goes to the right with a closed dot, and another starts at 7 and goes to the left with an open dot. These two rays overlap on the number line. Write and solve a compound inequality that represents the overlapping region, then describe the solution set in interval notation.
2. Solve: 4x - 9 > 15 OR 2x + 7 < -11
3. Hana is analyzing a compound inequality represented on a number line. The graph shows a ray starting at an open circle at 2 and extending to the left, AND a ray starting at a closed circle at 8 and extending to the right. What compound inequality does this graph represent? Write your answer in the form x < a OR x ≥ b (use appropriate inequality symbols).

…and 4 more problems

1. Kaia is a materials scientist developing a new alloy. The alloy's tensile strength S (in MPa) must satisfy two safety conditions for it to be used in aerospace applications: the tensile strength must be at least 16 MPa more than four times the carbon content C (in percent), but cannot exceed 30 MPa more than three times the carbon content. If the carbon content is fixed at 8%, write and solve a compound inequality to determine the acceptable range of tensile strengths for this alloy.
2. A pharmaceutical company is testing a new medication where the effective dosage range follows a compound inequality. The minimum effective dose is 2.5 mg per kg of body weight, and the maximum safe dose is 7.5 mg per kg. If a patient weighs w kilograms, write the compound inequality that represents all safe and effective dosages d (in mg) for this patient.
3. 2x² - 8x - 10 = 0

…and 4 more problems