Question

Pls show workings it due in a hour

Answer 1

The inequality describes all possible value of x is 14 < x < 32 ⇒ D

Explanation:

In any triangle:

• The sum of the lengths of any two sides must be greater than the length of the 3rd side

• The length of any side must greater than the difference of the lengths of the other two sides

• The difference of the other sides < The side < The sum of the other sides

In the given figure

∵ ABC is a triangle

∵ AC = 9 and BC = 21

∵ AB is the third side of the triangle

→ By using the rules above

∴ BC - AC < AB < BC + AC

∵ AB = x - 2

→ Substitute their values in the inequality above

∵ 21 - 9 < x - 2 < 21 + 9

∴ 12 < x - 2 < 30

→ Add 2 to the 3 terms

∴ 12 + 2 < x - 2 + 2 < 30 + 2

∴ 14 < x < 32

∴ The inequality describes all possible value of x is 14 < x < 32