Question

the side lengths of a triangle are 8, 11, 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 rule)

The sum of any two sides of a triangle must be greater than the third side. First, consider the sum of the two known sides:
$8 + 11 > x$
Simplify: $19 > x$

Step2: Apply inequality for smaller sides

The difference of the two known sides must be less than the third side:
$11 - 8 < x$
Simplify: $3 < x$

Step3: Combine inequalities

Combine the two results into a single inequality with $x$ only once.

Answer:

$3 < x < 19$