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

Explanation:

Step1: Understand the compound inequality

The inequality \( 64 < x < 68 \) means that \( x \) has to satisfy two conditions simultaneously: \( x \) is greater than 64 AND \( x \) is less than 68.

Step2: Analyze each option

• Option 1: \( x > 64 \) and \( x < 68 \) – This matches the meaning of \( 64 < x < 68 \), as both conditions must be true at the same time (using "and").
• Option 2: \( x > 64 \) or \( x < 68 \) – "Or" means either condition can be true, but \( 64 < x < 68 \) requires both to be true, so this is incorrect.
• Option 3: \( x < 64 \) and \( x < 68 \) – This would mean \( x < 64 \), which is not the original inequality, so incorrect.
• Option 4: \( x < 64 \) or \( x < 68 \) – This is equivalent to \( x < 68 \) (since if \( x < 64 \), it's already less than 68), which is not the original inequality, so incorrect.

Answer:

A. \( x > 64 \) and \( x < 68 \)