Question

the side lengths of a triangle are 11, 12, and $x$ units.
(the figure above gives only one possible configuration for the triangle.)
determine the possible values of $x$.
write your answer as an inequality.
use $x$ only once in your inequality.

Explanation:

Step1: Apply triangle inequality (sum > third)

$11 + 12 > x$
Simplify: $23 > x$

Step2: Apply inequality (11 + x > 12)

$11 + x > 12$
Simplify: $x > 12 - 11$ → $x > 1$

Step3: Combine inequalities

Merge $x > 1$ and $x < 23$

Answer:

$1 < x < 23$