Let's begin by identifying the lengths of the three sides of the triangle: length of side 1 = 17 length of side 2 = 2x - 1 (1 less than twice side 3) length of side 3 = x Now let's apply the Triangle Inequality Theorem to this triangle: side 1 + side 2 > side 3: 17 + 2x - 1 > x 16 + 2x > x 2x - x > -16 x > -16 (reject negative measurement) 2x - 1 > -33 (reject negative measurement) side 1 + side 3 > side 2 17 + x > 2x - 1 x - 2x > -1 - 17 -x > -18 x < 18 2x - 1 < 35 side 2 + side 3 > side 1 2x - 1 + x > 17 3x - 1 > 17 3x > 18 x > 6 2x - 1 > 11 Thus, we have our answers based on the value of x: 6 < x (length of side 3) < 18 11 < 2x - 1 (length of side 2) < 35