Question

if possible, write an inequality to describe the restrictions on x and which theorem was used to draw this conclusion. 2 < x < 29 by the hinge theorem 0 < x < 29 by the hinge theorem 2 < x < 29 by the hinge theorem converse 0 < x < 29 by the hinge theorem converse

Explanation:

Step1: Recall the hinge - theorem

The hinge - theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first triangle is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.
Let the two triangles have two pairs of congruent sides.
We know that \(0<2x < 58\) (since the angle in a triangle must be non - negative and we are comparing angles using the hinge - theorem).

Step2: Solve the inequality for \(x\)

Divide the inequality \(0 < 2x<58\) by 2.
For \(0 < 2x\), dividing by 2 gives \(0For \(2x < 58\), dividing by 2 gives \(x < 29\). So \(0

Answer:

\(0 < x < 29\) by the hinge theorem