Question

in order to qualify for a role in a play, an actor must be taller than 64 inches but shorter than 68 inches. the inequality \\(64 < x < 68\\), where \\(x\\) represents height, can be used to represent the height range. which is another way of writing the inequality?

\\(x > 64\\) and \\(x < 68\\)
\\(x > 64\\) or \\(x < 68\\)
\\(x < 64\\) and \\(x < 68\\)
\\(x < 64\\) or \\(x < 68\\)

Explanation:

Identify the given inequality

Using the Compound Inequalities knowledge point

$$ 64 < x < 68 $$

Split into separate inequalities

Using the Compound Inequalities knowledge point

$$ 64 < x \quad \text{and} \quad x < 68 $$

Rewrite the first inequality

Using the Compound Inequalities knowledge point

$$ x > 64 \quad \text{and} \quad x < 68 $$

Answer:

• (A) \(x > 64 \text{ and } x < 68\) (Correct answer)
• (B) \(x > 64 \text{ or } x < 68\)
• (C) \(x < 64 \text{ and } x < 68\)
• (D) \(x < 64 \text{ or } x < 68\)