Two sides of a triangle have lengths 8 and 17. Which inequalities represent the possible lengths for the third side, x?
9 < x < 17
9 < x < 8
8 < x < 17
9 < x < 25
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let x be the length of the third side
x must be greater than 17 - 8 = 9 units because if it were 9 units, then you'd have a straight line. If it were smaller than 9 units, then you wouldn't have a triangle.
x also must be smaller than 17+8 = 25 units to ensure you will have a closed/complete triangle
x > 9 and x < 25
9 < x and x < 25
9 < x < 25
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drawing a picture helps a lot if you don't/can't see this
a better way is to use rigid sticks to see this