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 \\) \\( 12 > x \leq 12.2 \\) \\( x > 12 \\) or \\( x \leq 12.2 \\) \\( x < 12 \\) or \\( x \leq 12.2 \\)

Explanation:

Step1: Analyze "longer than 12 cm"

"Longer than 12 cm" means \( x > 12 \).

Step2: Analyze "not longer than 12.2 cm"

"Not longer than 12.2 cm" means \( x \leq 12.2 \).

Step3: Combine the inequalities

To represent the length that fits, we combine the two conditions with "and" (since both must be true), so the inequality is \( 12 < x \leq 12.2 \).

Answer:

\( 12 < x \leq 12.2 \) (corresponding to the first option: \( 12 < x \leq 12.2 \))