Solving Compound Inequalities Effectively

What are the two types of compound inequalities?

• Greater than and less than

• Positive and negative

• Or and and

• Equal to and not equal to

In the inequality 2x - 5 < -11 or -3x + 14 ≤ 2, what is the first step to isolate x in the first inequality?

• Divide both sides by 2

• Multiply both sides by 2

• Add 5 to both sides

• Subtract 5 from both sides

Tags

CCSS.7.EE.B.4B

When solving -3x + 14 ≤ 2, what happens to the inequality sign when you divide both sides by -3?

• It stays the same

• It flips direction

• It becomes a greater than sign

• It becomes an equal sign

What is the interval notation for the solution x < -3 or x ≥ 4?

• (-∞, -3] ∪ [4, ∞)

• [−∞, -3) ∪ [4, ∞)

• (-∞, -3) ∪ (4, ∞)

• (-∞, -3) ∪ [4, ∞)

• (-∞, -3] ∪ (4, ∞)

What is the math symbol for the word 'or' in interval notation?

• ∩

• ∧

• ∨

• ∪

In the inequality 3x - 8 > -5 and ≤ 1, what is the first step to isolate x in the middle?

• Subtract 8 from all sides

• Add 8 to all sides

• Multiply all sides by 3

• Divide all sides by 3

What is the final solution for the inequality 3x - 8 > -5 and ≤ 1?

• 1 < x ≤ 3

• x > 1 and x ≤ 3

• x < 1 and x ≥ 3

• 1 ≤ x < 3

How do you express the solution 1 < x ≤ 3 in interval notation?

• [1, 3)

• [1, 3]

• (1, 3)

• (1, 3]

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