Question

Use the Hinge Theorem or its converse and properties of triangles to write and solve an inequality to describe the restriction on the value of x.
Please explain your work--I need to know how to work this problem more than I need an answer.

Answer 1

Answer:

The inequality is: $3x+2$

The result is: $x>1$

Step-by-step explanation:

1. According to the Hinge Theorem, when you have two triangles and two sides of both triangles are congruent, and the included angle of the first triangle is larger than the included angle of the other triangle, the third side of the first one is longer than the third side of the second one.

2. Keeping this on mind, as you can see in the figure, both triangles has two equal sides, and the included angle of the first one is larger than the angle of the second one:

 $38$°>$30$°

3. Therefore, the third side of the  first one is longer than the third side of the second triangle. So, you have the following inequality:

$3x+2$

4. Solve for $x$. Therefore, you obtain:

$2+7$