Question

to fit in an existing frame, the length, ( x ), of a piece of glass must be longer than 12 cm but not longer than 12.2 cm. which inequality can be used to represent the lengths of the glass that will fit in the frame?

( 12 < x leq 12.2 )

( x < 12 ) or ( x leq 12.2 )

( 12 > x leq 12.2 )

( x > 12 ) or ( x leq 12.2 )

Explanation:

Step1: Analyze the lower bound

The length \( x \) must be longer than 12 cm, which means \( x > 12 \).

Step2: Analyze the upper bound

The length \( x \) must not be longer than 12.2 cm, which means \( x \leq 12.2 \).

Step3: Combine the inequalities

Since \( x \) has to satisfy both conditions (longer than 12 and not longer than 12.2) at the same time, we combine the inequalities using "and", which is represented by the compound inequality \( 12 < x \leq 12.2 \).

Answer:

\( 12 < x \leq 12.2 \) (the first option among the given choices)