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 122 cm. Which inequality can be used to represent the lengths of the glass that will fit in the frame?

a) 12 < x < 122
b) x ≥ 12 and x ≤ 122
c) x > 12 or x ≤ 122
d) x < 12 or x > 122

Answer 1

The correct inequality to represent the lengths of glass that will fit in the frame is option (b) x ≥ 12 and x ≤ 122, which accounts for both the minimum and maximum length requirements.

Step-by-step explanation:

To determine which inequality would represent the lengths of glass that will fit in the frame, we need to translate the given conditions into mathematical terms. The length, x, must be greater than 12 cm and at the same time, it must be less than or equal to 122 cm. This can be denoted by the inequality 12 < x ≤ 122.

However, the options given do not include this exact inequality, so we choose the closest match, which would be (b) x ≥ 12 and x ≤ 122. This option correctly expresses both the lower and upper bounds for the length of glass that will fit in the frame.