High School

Write and solve an inequality for \( x \).

The figure shows triangle ABC. Point D lies on line AC. Segment BD is perpendicular to line AC. The length of segment BD is \( x + 3 \) units. The length of segment BC is 9 units.

A) \( x + 3 > 9; x < 6 \)
B) \( x + 3 > 9; x < -6 \)
C) \( x + 3 < 9; x < 6 \)
D) \( x + 3 < 9; x < 12 \)

Answer :

Final answer:

The correct inequality considering the lengths of the segments in the described triangle is x + 3 < 9, which simplifies to x < 6.

Explanation:

The question is asking to solve an inequality. According to the given conditions, the length of segment BD is x+3 units, and the length of segment BC is 9 units. We know in a triangle, any one side's length must be less than the sum of the other two sides' lengths. Hence, we have an inequality x+3 < 9. By solving this inequality, we get: x < 6. Therefore, option C) x + 3 < 9; x < 6 is the correct answer.

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