Solving Compound Inequalities with Fractions

What is the first step in solving a compound inequality?

• Subtract the same number from both sides

• Add the same number to both sides

• Divide both sides by the same number

• Multiply both sides by the same number

When solving the inequality 3x + 5 < 8, what is the value of x?

• x < 4

• x < 3

• x < 1

• x < 2

What happens to the inequality sign when you divide both sides by a negative number?

• It becomes an equal sign

• It changes direction

• It disappears

• It stays the same

How do you represent an open circle in interval notation?

• Using brackets []

• Using parentheses ()

• Using curly braces {}

• Using square brackets []

What is the interval notation for x < 1 or x ≥ 3?

• (-∞, 1) ∪ [3, ∞)

• (-∞, 1] ∪ (3, ∞)

• (-∞, 1) ∪ (3, ∞)

• (1, ∞) ∪ [3, ∞)

What is the first step in solving the inequality 7 ≤ 4x + 3 < 23?

• Divide all sides by 4

• Multiply all sides by 4

• Subtract 3 from all sides

• Add 3 to all sides

What is the value of x in the inequality 7 ≤ 4x + 3 < 23 after solving?

• 1 ≤ x < 5

• x ≤ 1 < 5

• x < 1 ≤ 5

• 1 < x ≤ 5

How do you represent a closed circle in interval notation?

• Using brackets []

• Using curly braces {}

• Using square brackets []

• Using parentheses ()

What is the interval notation for x between 1 and 5, including 1 but not 5?

• [1, 5)

• [1, 5]

• (1, 5)

• (1, 5]

What is the interval notation for x ≤ 6 or x > 10?

• (6, ∞) ∪ (10, ∞)

• (-∞, 6] ∪ (10, ∞)

• (-∞, 6] ∪ [10, ∞)

• (-∞, 6) ∪ [10, ∞)