## Geometry: Common Core (15th Edition)

$6 < x < 38$
According to the Converse of the Hinge Theorem, if two consecutive sides in a triangle are congruent to two consecutive sides in another triangle, but their third sides are not congruent, then the included angle that is opposite the longer side is the larger angle of the included angles in both triangles. Two sides in one triangle are congruent to two consecutive sides in another triangle. The angle opposite to the longer side has the greater value. Let's write an inequality reflecting this information: $32 > x - 6$ Let's add $6$ to each side of the inequality and flip the inequality around to simplify: $x < 38$ Also, $x - 6$ cannot be $0$ or less because you cannot have an angle that is $0^{\circ}$ or less, so let's set up the inequality to find out what the lowest value for $x$ can be: $x - 6 > 0$ Add $6$ to each side of the equation: $x > 6$ Let's write the range of $x$: $6 < x < 38$