Algebra 1 Linear Inequalities in One Variable Quiz: 10 Questions with Explanations

A \(x < 2\)B \(x \le 2\)C \(x \ge 2\)D \(x > 2\)

The circle is closed (2 included) and the ray points left, so x ≤ 2.

A \(x \ge -3\)B \(x > -3\)C \(x < -3\)D \(x \le -3\)

The circle is open (-3 not included) and the ray points right.

A \(x > 4\)B \(x < 7\)C \(x < 4\)D \(x < 5.5\)

Subtract 3 to get 2x < 8, then divide by 2. The symbol does not change.

A \(x \le -3\)B \(x \ge -3\)C \(x \le 3\)D \(x \ge 3\)

Dividing by -4 reverses the symbol and gives -3.

A \(x > 3\)B \(x < -3\)C \(x > -3\)D \(x < 3\)

Subtract 5: -x > -3. Multiply by -1 and reverse the symbol: x < 3.

A \(-2 \le x < 3\)B \(-2 < x < 3\)C \(-2 \le x \le 3\)D \(-2 < x \le 3\)

The open circle at -2 means -2 is excluded; the closed circle at 3 means 3 is included.

A 9 ridesB 10 ridesC 8 ridesD 37 rides

Solve 5r ≤ 42: r ≤ 8.4. She cannot buy part of a ride, so round down to 8.

A \(x = 5\)B \(x = 3\)C \(x = 2\)D \(x = 0\)

Substitute: 3(5) – 2 = 13 ≥ 10 is true. The other values give 7, 4, and -2, which are less than 10.

A \(x > 1\)B \(x > 4\)C \(x < 4\)D \(x > -4\)

Distribute: 3x – 3 > x + 5. Then 2x > 8 and x > 4. Forgetting to move 3 gives x > 1.

A \(x < -1 \text{ or } x \ge 3\)B \(x \le -1 \text{ or } x > 3\)C \(-1 < x \le 3\)D \(x > -1 \text{ or } x \le 3\)

Two rays pointing away from each other mean an or inequality. The open circle is at -1 and the closed circle at 3.